The confusion among Nornir, Dísir, Haminjur and Valkyries is so deep that I had to create a special documentation on them. Here it is.

1. About Norns

Here are the main texts that enable me to assert that the Norns are three giants maiden full of force and knowledge (‘therefore’ they know the runes), they promulgate örlög (destiny) and no one can oppose to their word. They are the sole hamigjur of the world, i.e., they take care of the destiny of the world as the hamingja associated to each family takes care of the destiny of the family members and brings them luck.

Völuspá
Verse 8

Teflðo í túni, teitir vâro [vöru], var þeim vettugis [vættergis] vant or gulli [ór golli], unz þriár komo, [kvömu] þursa meyar ámátcar [ámötcar] miök úr [ór] Jötunheimum.

They play ‘tafl’ in the hedge, of cheerfulness full, was to them naught lack of gold, [‘they did not lack gold’] until three come, giantesses [þurs = thurs, giant, jotun] maids (with) ‘giant strength’ much, out of the Jötuns’ dwellings.

Verse 19

Ask veit ek standa,	An ash I know it stands
heitir Yggdrasill,	it is named Yggdrasill,
hár batmr, ausinn	high tree, sprinkled
hvíta auri;	with white mud
þaðan koma döggvar	therefrom come the dews
þærs í dala falla,	that fall on the dale,
stendur æ yfir grænn	it stands always green, above
Urðarbrunni.	the source of Urdhr.

Verse 20

Þaðan koma meyjar	Therefrom come the maids
margs vitandi	much knowing
þrjár ór þeim sal [or sæ],	three, their dwelling [or ‘out of the sea that’]
er und þolli stendr;	stands under the tree;
Urð hétu eina,	Urdh is named one,
aðra Verðandi,	the other Verdhandi,
- skáru á skíði,	- they notched (scored) wood -
Skuld ina þriðju.	Skuld is the third.
Þær lög lögðu,	they set up the laws
þær líf kuru	they decided on the lives
alda börnum,	of the children of time (‘the children of man’)
örlög seggja.	they promulgate fate.

Vafþrúðnismál

Óðinn kvað:

48.

…

Hverjar ro þær meyjar, Who are these maids [Rask,Bugge: meyiar; Möbius, Jónsonn, Gering:meyjar]

er líða mar yfir, who pass by (glide) over the sea,

fróðgeðjaðar fara? knowledgeable of mind (they) travel [fróð-geð-jaðar: knowledgeable – mind – ed]

Vafþrúðnir kvað:

49.

Þriár þjóðár Three, (as if) powerful rivers, [Rask: þjóþár, Möbius, Bugge: þioðár; Jónsonn,: þjóðir, Gering: þjóþir. Gering provides also the 3 manuscript versions with ‘i’, ‘á’, ‘a’ and specifies that the manuscripts codex regius and codex arnamagnaeanus give ‘á’. Hence several different translations of this word. I read þjóð-ár : powerful rivers]

falla þorp yfir fall upon the village

meyja Mögþrasis, of the maids [daughters. Rask, Bugge:mejia; Möbius, Jónsonn, Gering:meyja] of Mögþrasir’s [“sonboaster:” he boasts of his sons],

[Þriár þjóð-ár falla yfir þorp meyja Mögþrasis = Three of Mögthrasir’s daughters, (as) powerful (as) rivers, fall on the village OR Three, (as) powerful (as) as rivers, fall on the village of Mögthrasir’s daughters]

hamingjur einar Hamingjur alone

þeira í heimi eru of whom (fem.) in the home [of the humans] are

þær með jötnum alask. though they with Jötuns brought up.

[sole Hamingjur who are in our world even though they are Jötunn born]

Hamðismál

30.
…

kveld lifir maðr ekki an evening lives the human not

eftir kvið norna. after the word of the Norns.
[No human survives to the Norns’ word]

Fjölsvinnsmál
47. …
Urðar orði (to) Urdh’s word

kveðr engi maðr, challenges no human

þótt þat sé við löst lagit. even when be by blunder is placed

[no human challenges Urdhr’s word even when it be that it is placed by blunder]

Forspjallsljóð or Hrafnagaldr Óðins

Note about this poem and Sólarljóð:

Ódhinn’s raven galdr (Hrafnagaldr Óðins) is not acknowledged as a real skaldic poem. It is obviously not as old as the classical skaldic poems. It is however not right to call it ‘forgery’ since it has been written in the 16th century and added in the Edda corpus by skaldic poetry lovers who wanted to keep their poetic tradition. A famous instance of them is Saemund, whose named has been used for the 19th c. name of the poetic Edda (then called Saemundar Edda). He is well-known for saving many ancient manuscripts and he classed it within the Edda. This poem is found in three serious editions of the poetic Edda, Rask’s (1818), Möbius’ (1860) and in famous Bugge’s (1867) ( http://etext.old.no/Bugge/ ) classed together with Sólarljóð as ‘tillaeg’ (supplements).

2.

Óðhrærir skyldi Óðhrærir should

Urður geyma Urðr keep

máttkat verja powerfully defend

mestum þorra. (of) greatest middle-winter months.

[this verse make of Urdhr the keeper of Ódhrærir, the mead of poetry – source of creativity. This recalls their role of “the world sole Hamingjur” - þorri is the fourth month of the winter, approximately between the 8th of January and the 8th of February]

2. About the ‘Disir’ (one dís, several dísir – note the accent)

The Dísir are divinities who are closer to humans than Norns are. Moreover, the word dís is often employed to speak of any woman. For example, Reginsmál S. 11 calls a girl: dís ulfhuguð = a wolf-spirited dís.

They attend some heroes, a bit as the hamingjur attend a family, but they not always bring them luck. They are rather representatives of their destiny, often a dire one. Grímnismál 53 describes a warrior who “has been chopped down by the edge of the swords” and who thus will join Valhöll. It comments: úfar ro [ = eru ] to dísir = rough are the dísir. In Reginsmál 24. the hero is described as surrounded by dísir:
tálar dísir, treacherous dísir

standa þér á tvær hliðar stand they at two sides

ok vilja þik sáran sjá. and will you sore see.

They are thus not specially beneficial (contrary to what Snorri asserts when he draws the difference between Nornir and Dísir) but they attend a hero’s fate. Moreover, several poems say say “þér dísir” = “your dísir” when someone addresses to the hero. Here are three examples:

Atlamál in grænlenzku, S. 28:

ek kveð aflima I say cut off

orðnar þér dísir. the words your [‘thine’] dísir [your dísir cut off the words, i.e., your destiny]
Gunnars slagr s. 9 (thought to be due to Gunnar Pálsson 1714-1781, following Viga-Glums saga) says:

Hugða ek þér dísir … Minded I your dísir …
Sólarljóð s. 25 :

Dísir bið þú þér The Dísir bide thou your

dróttins mála of the Lord’s words

vera hollar í hugum; (that) they are faithful in spirit;

[Pray your Dísir to stay faithful to the spirit of the Lord’s words;]

They also have a special role toward the delivering women. As said by Sigrdrífumál 9.
Bjargrúnar skaltu kunna, Saving-runes shall (you) know

ef þú bjarga vilt if you (‘thou’) save will

ok leysa kind frá konum; and loose the child from women ;

á lófum þær skal rista on the palms they shall carve

ok of liðu spenna and on the joint to clasp

ok biðja þá dísir duga. and beg then the Dísir to help.

And this special role makes it possible to understand that the skald who wrote Fáfnismál (stanzas 12. and 13) did not ‘confuse’ Norns and Dísir. As it happens so often in skaldic poetry, he called the Dísir with the name of ‘Norns’, because the context eliminated any risk of error. It is obvious that he speaks of the Dísir when he says:
12.
…
hverjar ro þær nornir, who are these Norns

er nauðgönglar ro who distress-walking are

ok kjósa mœðr frá mögum. and choose the mothers from the sons?

And this is why the Dísir, not the Norns, are said to be of several kinds:
Fáfnir kvað [said]:
13.
Sundrbornar mjök Different origins many

segi ek nornir vera, say I the Norns be

eigu-t þær ætt saman, have-not them family same

sumar ro áskunngar, some are áss akin

sumar alfkunngar, some are elf akin

sumar dœtr Dvalins. some are daughter of Davlin [a dwarf].

Thus, whereas Norns are three giantesses, the Dísir are of varied origin and there is an unspecified, but large number of them.
Another objective difference between Norns and Dísir is that there has been a religious ceremony devoted to the Dísir, the dísablót, while we never hear of any ‘Nornablót’. Norns are thus further away from humans, they seem to deal rather with humankind and our world tha, with individual fates.
It thus seems that the Dísir look much more as Hamingjur than to the Norns. The difference between the two is that a Hamingja ‘specializes herself’ in bringing luck to a family whereas the Dísir express destiny, be it good or bad.

3. The world of the Norns

Have again a look at Völuspá s. 19 and 20 to remember that they live close to Urdhr’s Spring which lies just above Yggdrasil’s roots. They are thus found between Ásgardh and the worlds located under the Yggdrasil’s roots. They are said to leave ór þeim sal [or sæ] er und þolli stendr; (out of their residence [or : ‘out of the salted sea ‘] standing under the tree). I personally prefer the old version which gives sal but I do not want to enter now a debate about sal vs. sæ. At any rate, sæ is obviously not absurd : Their dwelling place is often called Urdhr's fountain and that makes of them water sprites. Morever, remember that in Vafþrúðnismál, s. 48, Óðinn asks Vafþrúðnir:
…
Hverjar ro þær meyjar, Who are these maids [Rask,Bugge: meyiar; Möbius, Jónsonn, Gering:meyjar]

er líða mar yfir, who pass by (glide) over the sea,

fróðgeðjaðar fara? knowledgeable of mind (they) travel? [fróð-geð-jaðar: knowledgeable – mind – ed]

This still increases the feeling that they would be water goddesses. To conclude this argument, note that Fáfnismál, s. 11, now without ‘confusing’ Norns and Dísir, states that Fáfnir says:
Norna dóm The Norns’ judgment court

þú munt fyr nesjum hafa you [‘thou’] must in front of the nesses have (a nes is a promontory that ends in the sea or a lake as in Loch Ness)

ok örlög ósvinns apa, and örlög of an unwise ape [a big fool],

[you (‘thou’) must, in front of the rocks in the lake, receive the Norns’s judgment and (receive) a big fool’s destiny.]

Thus, it is clear that the world of Norns is primarily a watery world and that, according to Fáfnismál, they even give their word while standing above water. This does not recalls the beautiful Greek Aphrodite ‘Anadyomenes’, since they are stern judges upright on water.

This place is also a place of intense meditation where magic takes its source. This is why I recmind you of stanza 111 of Hávamál:

Mál er at þylja It is time to mumble (charms) [most often translated speak or sing, see Evans’ comment below]

þular stóli á from the wise-men’s seat [most do not allude to the link between þulr and ‘warlock’, see Evans]

Urðarbrunni at, near Urdhr’s fountain,

sá ek ok þagðak, I saw and was silent,

sá ek ok hugðak, I saw and was thoughtful,

hlydda ek á manna mál; I heard (or : I give way to) the men’s words;

of rúnar heyrða ek dæma, of the runes I heard the story

né of ráðum þögðu not of advice were them silent [they were not silent when providing advice –runes or men?]

Háva höllu at, near Highs’ hall,

Háva höllu í, in Highs’ hall,

heyrða ek segja svá: I heard said this:

This is a place where quietness and awareness enable us to acquire knowledge by “hearing the story of the runes”. The poem also says to us that the seat of wisdom is close to both

the fountain of Urdhr and the hall of Ódhinn. A last remark: do not be confused by the skald’s style ,when he plays on ‘near to’ and ‘into’ in the two lines before the last. We should understand that a line of the thinking ends after “near Highs’ hall” and that a new line of thinking starts with “in Highs’ hall,” which is connected to verse 112.

It is slightly amusing that the Christian poem Sólarljóð parallels Hávamál in giving us a description of the Norns’ world. After asking someone to pray his Dísir to listen to the Lord’s words, he claims, s. 51, that he visited the Norns’ world:
Á norna stóli On the Norns’ chair

sat ek níu daga, sat I nine days,

þaðan var ek á hest hafinn; from there was I on the horse high;

gýgjar sólir the witch suns

skinu grimmliga shining fearfully

ór skýdrúpnis skýjum. out of cloud-dripper clouded.

[the witch-suns, fearfully shining, clouded by ‘dripping down’ clouds]

We see that a Christian whose head was still full of Pagan stories the Norn’s world is lightened by a strange sun from which clouds rain down. The claim that he “sat nine days on the Norns’ chair” parallels Ódhinn’s nine days suffering when he was hanging from the world’s tree. You must also realize that the Hávamál says that Ódhinn was hanged in a vindgameiðr and that meiðr means ‘tree’ and ‘gallows’ as well. The gallows are also called Ódhinn’horse, thus Sólarljóð’s “high horse” is yet another allusion to Ódhinn. The Christian skald seems to hint at some common feature among the Norns and Ódhinn, all of them demons by his book.

4. What differences among Norns, Dísir and Valkyries?

First thing, there is no reason why the Norns or the Dísir could be even compared to the Valkyries. Valkyries are Ódhinn’s servants who carry out his demands on the battlefield. Ódhinn, not them, chooses who will die. The best proof of what I am stating is Sigrdrífa’s fate who has been so heavily punished because she refused to obey one of Ódhinn’s orders.
I already produced several poems that draw a clear line between the Norns and the Dísir. The only large confusion is due to Fáfnismál (verses 12. et 13) which calls ‘Norns’ the Dísir. As I said already, I believe it to be a poetical effect of the Skald who used ‘norn’ as a heiti (= an equivalent word) for ‘Dís’, a classical figure of style in skaldic poetry. The skald knew tha any ‘knowledgeable’ reader would immediately spot his heiti, and appreciate this fine point.
Inversely, no skald ever uses the way of speech: “your Norns” while I gave you three examples of “your Dísir.”
Besides, here are a few ways of speaking of the Norns and the Dísir:
Reginsmál
2 : aumlig norn ‘a wretched norn’ … [shaped my fate]
Fáfnismál 44 : [Everything happens …] fyr sköpum norna ‘in front of the fatality of the Norns’
Sigrdrífumál 17 : [Runes are carved …] á nornar nagli ‘on the nail of the Norn’
[and adds that the Dísir’s help has to be obtained for a healthy delivery.]

Sigurðarkviða in skamma 7 : ljótar nornir skópu oss langa þrá. ‘awful Norns shaped my long throe (longing)’.
Grógaldr
4. [Possibly…] skeikar þá Skuld at sköpum ‘you [or he] swerve(s) then Skuld at shaping [your destiny]’
7. [I sing magical words so that …] Urðar lokur haldi þér öllum megum, ‘Urðr’s [or weird] protections hold you all around’.
Guðrúnarhvöt 13 : gröm vark nornum, ‘angers was I at the Norns’.
Hlöðskviða 32 : illr er dómr norna. ‘bad is the Norn’s sentence’.

People complain of the Norns, they even hate them , they however always are the ones who shape destiny. Inversely, this is never stated of the Dísir, except what I already pointed at, people simply complain of them:
Reginsmál 24 : tálar dísir … treacherous dísir …
Grímnismál 53 : úfar ro dísir, rough are the dísir,

Finally, Hrafnagaldr Óðins speaks of the three types of Goddesses and it says of them:

1 : vísa nornir … þrá valkyrjur ‘Norns show … wait impatiently the Valkyries’.
6 : dís forvitin ‘the inquisitive dís’

All in all, you can see by yourself that there is only one good reason for confusing Norns and Dísir: this is the (perhaps too much) clever heiti found in Fáfnismál (verses 12. and 13.).

Supplementary references

David A. H. Evans

produced a detailed discussion of Hávamál in the VIKING SOCIETY FOR NORTHERN RESEARCH TEXT SERIES (A. R. Faulkes and P. G. Foote Eds.), 1986. Here are his comments of verse 111.

111 On this obscure and much-debated strophe see p. 26 above and Hollander 2, 282-7.

2 þulr seems to mean something like ‘sage’ or perhaps ‘seer’. The word recurs in 134, where Loddfafnir is exhorted not to laugh at a ‘hoary þulr’, since the old often speak wisely, and in 80 and 142 the runes are said to have been coloured by fimbulþulr, the mighty þulr (presumably Óðinn); the association with age also appears in the other two occurrences in the Edda: inn Hára þul, referring to Reginn, in Fáfnismál 34 and inn gamli þulr, used of Vafþrúðnir, in Vafþr. 9. In other poems the word is applied once to the legendary hero Starkaðr, once to the ‘wizard poet’ Þorleifr jarlsskáld, and once by the poet Rögnvaldr kali to himself; it does not occur in prose, but an early ninth-century Danish runic inscription from Snoldelev commemorates one Gunnvaldr, son of Hróaldr, þulr at Salhaugar (now Sallev), as though this were a recognized public office. The OE cognate þyle is used to gloss orator and also, it seems, scurra and histrio (see PMLA 77 1962)

2). and þelcræft (evidently for *þylcræft) glosses rethoric, and in Beowulf Unferth, a courtier of the Danish king Hrothgar, at whose feet he sits, is called Hroþgüres þyle. The Norse verb þylja. which is doubtless derived from the noun, sometimes appears to mean ‘chant, proclaim’, as in the present passage. and sometirnes ‘mumble to oneself (especially of the mumbling of spells, hidden wisdom etc.). cp. st. 17 above: there is also a noun þula ‘poetic catalogue, rigmarole’. There has been much speculation as to the original function of the þulr: most probably he was some kind of publicly acknowledged wise man, repository of ancient lore and credited with prophetic insight. But since the concept was evidently essentially prehistoric and already obsolescent at the time of our oldest records, certainty is impossible. For further discussion see E. Noreen 2.19-26. W. H. Vogt ‘Der frühgermanische Kultredner’ APhS II (1928) 250-63. Axe1 Olrik ‘At sidde pa Höj’ Danske Studier 1909, 1-10. and H. M. and N. K. Chadwick The Growth of Literature 1 (Cambridge 1932) 618-21.

3 Urþar brunni at - editors differ as to whether this should be taken with what precedes or with what follows. But since the strophe as a whole is involved in so much obscurity it seems risky to break the regular pattern of Ljóðaháttr by placing a stop after the first ‘long line’ (i.e. at the end of line 2); the only parallel would be 69, but there a break occurs at the end of line 3 as well. The Urðar brunnr is stated in Völuspá 19 to lie beneath the evergreen ash Yggárasill, and Snorri says in the Prose Edda (Gylfaginning ch. 15) that þribja rót asksins stendr á himni, ok undir þeiri roter brunnr sá, er mjök er heilagr, er heitir Urðarbrunnr. Þar eigu guðin dómstað sinn. In a fragment of a Christian poem the tenth century skáld Eilífr Guðrúnarson speaks of Christ as having his station sunnr at Urðar brunni (Skj. í 144), evidently a Christian appropriation of the concept of the Well of Fate as the seat of wisdom.

.

Grímnismál

53.

Eggmóðan val the edge-mowed slain

nú mun Yggr hafa, now will Yggr have,

þitt veit ek líf of liðit; to you grant I life of little

úfar ro [=eru] dísir, rough are the dísir,

nú knáttu Óðin sjá, now you do Óðin see

nálgastu mik ef þú megir. come near to me if you can.

Reginsmál

2.

Andvari heiti ek, Andvari named I

Óinn hét minn faðir, Óinn named my father,

margan hef ek fors of farit, many heaved I a stream in my travels

aumlig norn a wretched norn

skóp oss í árdaga, shaped me in ancient times

at skylda ek í vatni vaða. that bind I in waters vade.

Fáfnismál

Fáfnir kvað:

11.

Norna dóm The Norns’ judgment court

þú munt fyr nesjum hafa you [‘thou’] must in front of the nesses have (a nes is a promontory that ends in the sea or a lake as in Loch Ness)

ok örlög ósvinns apa, and örlög of an unwise ape [a big fool],

[you (‘thou’) must, in front of the rocks in the lake, receive the Norns’s judgement and (receive) a big fool’s destiny.]

í vatni þú druknar in the water ‘you’ being drowned

ef í vindi rœr, if in the wind you row

alt er feigs forað. whole is fey [or death-bound] abyss [or dangerous situation].

[you will be drowned in the water if you row in the wind, the abyss of the fey is complete (for you)]

[[Note: in a manuscript dated 1660-1680, we find a Þrideilur Rúna giving the following explanation with rune Is: “feigur: qvi jam fatali morti appropingvat” (who already from fated death approaches), “forad . puteus hians” (abyss, wide hole)] ]

Sigrdrífumál

17.

[Runes are carved …]

á nornar nagli on the nail of the Norn

ok á nefi uglu. and on the beak of the owl.

Grógaldr

4.

…

ef þat verðr, if that would (be)

at þú þinn vilja bíðr, at you your wish abides

ok skeikar þá Skuld at sköpum. and you [or he] swerve(s) then Skuld at shaping [your destiny]

7.

Þann gel ek þér annan, Thus sing/howl I for you secondly

ef þú árna skalt if you earn shall [if you shall earn (to be)]

viljalauss á vegum: will-less in the ways

Urðar lokur Urð’s [or weird] protections

haldi þér öllum megum, [that] hold you all around,

er þú á sinnum sér. while you in heavy walk.

Guðrúnarhvöt

13.

Gekk ek til strandar, Went I until the strand

gröm vark nornum, angers was I at the Norns

vilda ek hrinda wanted I to kick

stríðgrið þeira; the place of their calamity;

hófu mik, né drekkðu, they [the waves] raised me, did not drink me,

hávar bárur, the high waves,

því ek land of sték, because I land stepped [I stepped on land]

at lifa skyldak. to live I shall.

Hamðismál

Hamðir kvað:

28.

[We killed our brave brother …]

- hvöttumk at dísir, - - the Dísir had us whetted [encouraged] -

Sörli kvað:

29.

…

sem grey norna, as the Norns’ dogs [wolves]

þá er gráðug eru those greedy are,

í auðn of alin. in destruction the measure

30.

…

kveld lifir maðr ekki an evening lives the human not

eftir kvið norna. after the word of the Norns.

[No human survives the Norns’ word]

Hlöðskviða

32.

Bölvat er okkr, bróðir, ‘Baled’ [misfortune carriers] are we, brother,

bani em ek þinn orðinn, bane am I of your ‘word’,

þat mun æ uppi, that will ever up (known)

illr er dómr norna. bad is the Norn’s sentence.

Forspjallsljóð or Hrafnagaldr Óðins

1.

Alföðr orkar, Able is Allfather [Óðinn]

álfar skilja, Elves analyze

Vanir vitu, Vanir [ancient Gods] know

vísa nornir, Norns show

elr íviðja, begets Iviðja

aldir bera, carry the humans

þreyja þursar, wait painfully the Thurses

þrá valkyrjur. wait impatiently the Valkyries

2.

Óðhrærir skyldi Óðhrærir should

Urður geyma Urðr keep

máttkat verja powerfully defend

mestum þorra. (of) greatest middle-winter months.

[this verse make of Urdhr the keeper of Ódhrærir, the mead of poetry – source of creativity. This recalls their role of “the world sole Hamingjur”]

6.

…

dís forvitin the dís inquisitive

Sólarljóð

(a Christian skaldic poem)

25

Dísir bið þú þér The Dísir bide you them

dróttins mála of the Lord’s words

vera hollar í hugum; (that) they are faithful in spirit;

[Pray the Dísir to stay faithful to the spirit of the Lord’s words;]

51

Á norna stóli On the Norns’ chair

sat ek níu daga, sat I nine days,

þaðan var ek á hest hafinn; from there was I on the horse high;

gýgjar sólir the witch suns

skinu grimmliga shining fearfully

ór skýdrúpnis skýjum. out of cloud-dripper clouded.

[the witch-suns, fearfully shining, clouded by ‘dripping down’ clouds]

Gunnars Slagr (Gunnar’s Melody)

(Most probably due to Gunnar Pálsson 1714-1781, inspired by from Viga-Glums saga)

9. [I saw a spear red with your blood, a gallows ready for Giuki's son]

Hugða ek þér dísir Minded I your dísir

heimboð gøra. a ‘home-bidding’ build.

Munu ykkr brœðrum Shall for your brothers
búin vélræði. prepared artifice-rules

11.

Oss hafa nornir For us have the Norns

aldr um lagit, a time around laid

örfum Gjúka for heirs Gjúka’s

at Óðins vild. at Óðinn’s liking.