> Ólafur kvaðst það mundu af taka.
> Olaf stated-for-himself that (he) would choose.

Unlike English <that>, <þat> is always a pronoun and never a
conjunction; the closest counterpart to <that> as a
conjunction is the ON conjunction <at>.

> Olaf said of himself (they) would choose??? it.
> Ólafr declared-of-himself (that he) would choose that.

<Taka> has such a wide range of idiomatic usages that we
probably shouldn't expect the dictionaries to give a
complete catalogue. Zoëga's glosses notwithstanding, it
seems pretty clear that Ólaf was saying that he'd do it. I
note that another edition has <upp taka>, which can
definitely mean 'to do/undertake (something)'.

> Gunnhildur lagði mikil mæti á Ólaf er hún vissi að hann
> var bróðurson Hrúts.

> Gunnhild took a fancy for Olaf when she knew that he was
> Hrut's nephew. (Z. mæti - leggja m. á e-n, to take a fancy
> for)

> Gunnhild took a great fancy to Olaf when she learned that
> he was Hrut's nephew.

> Gunnhildr took a great fancy to Ólafr (leggja mæti á e-n,
> under mæti, Z2) when she knows (sees) that he was Hrútr’s
> nephew (brother’s-son).

Rob and Grace are right in reading <vissi> as past tense;
here it seems to be a mixture of Z2 'know' and Z3 'see, try
to find out', something like 'found out'.

> En sumir menn kölluðu það að henni þætti þó skemmtan að
> tala við Ólaf þótt hann nyti ekki annarra að.

> But some men said that to her it-seemed although amusement
> to speak to Olaf thought he (advantage) not to another.

> And some people said it that she seemed still amused to
> talk with Olaf though he need not other (associations).

> But some persons (men) said that, that (it) would-seem to
> her still an amusement to talk to Ólafr even-if he
> should-benefit nothing from others in (it).(?)

'Even if he had not the benefit of others'. This must be a
reference to the previous sentence, which attributed her
fancy to his relationship to Hrút: some thought that she'd
have fancied him for himself even if he hadn't had the
benefit of being related to one of her favorites.

> Ólafur svarar: "Ferð á eg á höndum mér að fara vestur um
> haf og þætti mér mikið undir að þú ættir hlut í að sú yrði
> farin sumarlangt."

> Olaf answers: "I have a journey in my hands (i.e., at
> hand) to go westward across (the) sea and it-seemed to me
> very worth much that you families share in to such become
> gone during-the-summer.

> Olaf answers, "I have a journey on my hands to go west
> over (the) sea and seems to me much depends that you had a
> part?? in (it) that it is made?? during the summer."

> Ólafr answers: “I have a journey on my hands (ie to
> undertake) to go west across (the) sea and (it) would-seem
> to me worth much (see vera mikit undir, under undir, Z4)
> that you should-have a part in (it)(so) that she (ie the
> journey) should-become travelled (undertaken)
> during-the-summer.”

Another possibility is to read it as if there were a comma
after <hlut í>, so that <at þú ættir hlut í> and <at sú yrði
farin sumarlangt> become parallel clauses: 'and it would
seem to me worth much [i.e., I greatly desire] that you
should have a part in (it) (and) that it should be
undertaken during the summer'.

> Örn bað Ólaf þess ekki fýsast, kvaðst ekki vita vonir
> skipa þeirra er um haf vestur mundu ganga.

> Orn asked Olaf (to) not desire this, stated-for-himself
> not (to) know (vonir?) those ships which across (the) sea
> westward would go.

<Vonir> is for older <vánir>, plural of <ván> 'hope,
expectation'. The closest parallel in Z. is the example
<hann vissi enga ván, at> 'he had no expectation, that'. CV
has <vita sér engis ótta vánir> 'to apprehend no danger',
which I think might be more literally rendered 'to expect
for himself no dreadful thing'.

> Orn bade Olaf not to be eager, said of himself not to know
> (the) usual ships which would go west over (the) sea.

> Örn asked Ólafr not to desire that, declared-of-himself
> not to know (have) expectation of those ships which would
> go west across (the) sea.

I think rather 'said that he did not expect the ships that
would go west across [the] sea'.

> Gunnhildur gekk á tal þeirra og mælti: "Nú heyri eg ykkur
> það tala sem eigi hefir fyrr við borið, að sinn veg þykir
> hvorum."

> Gunnhild went to their talk and spoke: "Now I hear you-two
> that talk as have not previously born with, that one's way
> is-thought who."

> Gunnhild went to speak with them and spoke, "Now I hear
> both of you speak it as has not previously happened that
> each thinks his own way."

> Gunnhilde went into (joined) their conversation and spoke:
> “Now I hear from you that talk which has not before
> happened (see bera við, Z.II.3), that (it) seems each way
> to (the) other (ie they cannot agree, see under sinn,
> Z5).”

If <tala> were a noun here, it would have to be in the
accusative, but the accusative of neuter <tal> is <tal>, and
that of feminine <tala> is <tölu>. This has to be an
accusative (<ykkr>) plus infinitive (<tala>) construction,
which occurs regularly after verbs of saying, thinking, and
experiencing (e.g., <heyra>): 'Now I hear you two saying
that which has not happened before'.

> Segir Ólafur þá ætlan sína og svo hvað honum lá
> við, að Mýrkjartan konungur var móðurfaðir hans.

> Then Olaf tells his plan and also what he was on the verge
> of (doing), that King Myrkjartan was his
> maternal-grandfather. (Z. liggja 8 - e-m liggr við e-u,
> one is on the verge of)

> Olaf declares then his intention and also what lay at
> stake that King Myrkjartan was his grandfather (on his
> mother's side).

> Ólafr says then his opinion and also what lay with him
> (what was on his mind, what he was on the verge of, see
> liggja við e-u, Z8), that King Mýrkjartan was his
> maternal-grandfather.

It can't be 'on the verge of': that takes the dative of the
thing as well as of the person, and <hvað> isn't a dative.
Grace is on the right track, but the closest model seems to
be <en mér liggr hér nú allt við> 'it is all important to
me' in CV s.v. <liggja> (B). It's not entirely clear to me
whether the final clause goes with <segir> or with what
immmediately precedes it, but I lean towards the former
interpretation. 'Then Ólaf tells [her] his intention and
thus what was important to him, [and] that king Mýrkjartan
was his maternal grandfather.'

> Og er Örn einn nefndur með Ólafi til ferðarinnar.
> Also is Orn one named with Olaf for the journeys.
> And Orn alone is named with Olaf for the journey.
> And Örn alone is named along-with Ólafr for the journey.

I.e., Örn and Ólaf are the only members of the company whose
names are mentioned.

> Þetta lið var allvel búið.
> This ship was very-well built.
> That crew was very well prepared.
> This force was very-well equipped.

I'd go with Alan's 'equipped': this whole bit is about
Gunnhild's financial generosity in outfitting the
expedition, whereas 'well prepared' is most naturally read
as a statement about the training or state of mind of the
crew.

> Haraldur konungur og Gunnhildur leiddu Ólaf til skips og
> sögðust mundu leggja til með honum hamingju sína með
> vingan þeirri annarri er þau höfðu til lagt.

> King Harold and Gunnhild conducted Olaf to (the) ship and
> declared-of-themselves (that they) would furnish with him
> his good-fortune with their friendship one-of-the-two
> which they had furnished.

> King Harald and Gunnhild lead Olaf to (the) ship and said
> they would contribute to him their luck with their other
> friends?? who they had contributed to.

> King Haraldr and Gunnhildr lead Ólafr to (the) ship and
> said-of-themselves (that they) would deliver to him their
> guardian-spirit (good fortune) along-with their other
> friendship which they had put forward.

After reading CV s.v. <hamingja>, I've the impression that
it's the luck/good fortune imparted by the guardian spirits
that they're adding to their other gestures of friendship;
the guardian spirits themselves are intrinsically theirs.

Brian