> Þórarinn hljóp að Þorbirni og hjó með sverði í höfuðið og
> klauf ofan í jaxla.

> Thorarinn attacked Thorirn and struck (him) with a sword
> in the head and split down to (the) molars.

> Thorarinn ran towards Thorbjorn and struck at (his) head
> with a sword and cleaved (it) down to the jaw.

Þórarin ran at Þorbjörn and struck with (his) sword into the
[i.e., Þorbjörn’s] head and clove (it) down to (the) molars.

> Eftir það sótti Þórir Arnarson að Þórarni við þriðja mann.

> Next, Thorir Arnarson attacked Thorarn with two men. (Is
> there any way grammatically to tell if the two unnamed men
> are attacking or being attacked? That is, are the two men
> with Thorir or with Thorarn?)

> After that Thorir Arnarsson attacked as the third man.

After that Þórir Arnarson attacked Þórarin with two (other)
men.

Rob: I'm not sure that I've seen the <við n-th mann>
construction used anywhere but the subject. (In this case
there's also the fact that Þorbjörn's group outnumbered
Þörarin's.)

> Hallsteinn sótti Álfgeir við annan mann.
> Hallstein attacked Alfgeir with another man.
> Hallsteinn attacked Alfgeir with another man.

Hallstein attacked Álfgeir with another man.

> Oddur Kötluson sótti félaga Álfgeirs við annan mann.

> Oddr Kotluson attacked Alfgeir's companions with another
> man.

> Odd Katla’s son attacked Alfgeir’s comrade with another
> man.

Odd Kötluson attacked a companion of Álfgeir with another
man.

Accusative <félaga> could be either singular or plural, but
since Odd was on the side with the numerical advantage, I
think it likely that this was a two-on-one deal.

> Þrír förunautar Þorbjarnar sóttu tvo menn Þórarins og var
> bardagi þessi sóttur með miklu kappi.

> Three travelling companions of Thorbjarn attacked two of
> Thorarin's men and this battle was prosecuted with much
> ardor.

> Three of Thorbjorn’s comrades attacked two of Thorarinn’s
> men and this battle was fought with great intensity.?

Three of Þorbjörn’s companions attacked two of Þórarin’s
men, and this fight was conducted with great zeal.

> Þeirra skipti fóru svo að Þórarinn hjó fót af Þóri þar er
> kálfi var digrastur en drap báða förunauta hans.

> Their fights went so that Thorarinn hacked off Thori's
> foot there where (the) calf is thickest and killed both
> his companions.

> Their fights went so that Thorarinn struck Thori’s foot
> off there where the calf was thickest and slew both of his
> comrades.

Their fights turned out thus, that Þórarin cut off Þórir’s
leg where the calf was thickest and killed both of his
companions.

> Hallsteinn féll fyrir Álfgeiri sár til ólífis en er
> Þórarinn var laus rann Oddur Kötluson við þriðja mann.

> Hallstein fell before Alfeir, mortally wounded, and when
> Thorarinn was free Oddr Kotluson ran with two men.

> Hallstein fell wounded to death by Alfgeir and when
> Thorarinn was free Odd Katla’s son ran as the third man.

Hallstein fell before Álfgeir, wounded to (the) death, but
when Þórarin was free [i.e., when he'd taken care of his
opponents and was free to take on more], Odd Kötluson fled
with two men.

> Hann var eigi sár því að eigi festi vopn á kyrtli hans.

> He was not wounded because a weapon did not stick fast to
> his shirt.

> He was not wounded because no weapon touched his kyrtle.

He was not wounded, because weapons did not bite on his
tunic.

> Allir lágu eftir aðrir förunautar þeirra.
> All left undone their other companions.
> All other comrades lay behind them.

All their other companions lay behind [i.e., dead on the
field].

> Látnir voru og báðir húskarlar Þórarins.
> Both Thorarin's house servants were also left.
> Also slain were both Thorarinn’s house servants.

Both of Þórarin’s house-carls were also dead.

> Þeir Þórarinn tóku hesta þeirra Þorbjarnar og ríða þeim
> heim og sáu þeir þá hvar Nagli hljóp hið efra um hlíðina.

> They, Thorarinn (and his side), took the horses of
> Thorbjarn and ride them home, and they saw where Nagli ran
> the highest across the mountain slope.

> They Thorarinn (and co.) took their,Thorbjorn’s (and
> companions’) horses and ride them home and they saw then
> where Nagli ran the uppermost on the ridge.

Þórarin & Co. took the horses of Þorbjörn & Co. and ride
them home, and then they saw where Nagli ran high above on
the hillside.

> Og er þeir komu í túnið sáu þeir að Nagli var kominn fram
> um garðinn og stefndi inn til Búlandshöfða.

> And when they came to the hayfield they saw that Nagli had
> come forward across the yard and headed in to
> Bulandshofda.

> And when they came in the home field, they saw that Nagli
> had come forward over the ridge and turned in to Buland’s
> headland.

And when they came to the home meadow, they saw that Nagli
had come forth around the farm enclosure and headed inland
towards Búlandshöfuð.

> Þar fann hann þræla Þórarins tvo er ráku sauði úr
> höfðanum.

> There he found two of Thorarin's thralls who drove sheep
> out of the cape.

> There he met Thorarinn’s two thralls who drove sheep out
> of the headland.

There he met two of Þórarin’s thralls, who were driving
sheep from the headland.

> Hann segir þeim fundinn og liðsmun hver var.

> He tells them the discovery and (the) odds that were.

> He tells them of the fight and odds which existed.

He told them (of) the battle and what odds (there) were
[i.e., had been].

This is another reference to the numerical superiority of
Þorbjörn's group.

> Kallaðist hann víst vita að Þórarinn og hans menn voru
> látnir og í því sáu þeir að menn riðu heiman eftir
> vellinum.

> He said for himself (to) know for sure that Thorarinn and
> his men were left and in that they saw that men rode from
> home across the field.

> He said of himself certain to know that Thorarinn and his
> men were dead and at that they saw that men rode from home
> along the plain.

He said that he knew for certain that Þórarin and his men
were dead, and just then they saw that men rode from home
across the field.

> Þá tóku þeir Þórarinn að hleypa því að þeir vildu hjálpa
> Nagla að hann hlypi eigi á sjó eða fyrir björg.

> Then they, Thorarinn (and his men), began to gallop
> because they wanted to help Nagli that he did not run to
> (the) sea or for help.

> Then they Thorarinn (and co.) began to run because they
> wanted to help Nagli that he not run to the sea or for
> shelter? (P&E have cliff?)

Then Þorarin & Co. began to gallop, for they wished to help
Nagli, that he not leap into the sea or over [the] cliffs.

<Björg> is the nom./acc. plur. of <bjarg> 'a precipice, a
cliff'; the expression <hleypa fyrir björg> can be found at
<fyrir> Z(II.3).

> Og er þeir Nagli sjá að mennirnir riðu æsilega hugðu þeir
> að Þorbjörn mundi þar fara.

> And when they see Nagli that the men rode terrifically; it
> seemed to them that Thorbjorn would go there.

> And when they, Nagli (and the shepherds) saw that the men
> rode furiously, they thought that Thorbjorn would be
> riding there.

And when they [i.e., the thralls] and Nagli saw that the men
rode furiously, they thought that Þorbjörn must be going
there.

> Tóku þeir nú rás af nýju allir inn til höfðans og runnu
> þar til er þeir koma þar sem nú heitir Þrælaskriða.

> They took to their heels again all in to the cape and ran
> to where they came there where now is called Thrallskrida.

> Now they all began anew to run in to the headland and ran
> until they come there which is now called Thrall’s scree.

Now they all took off running again, in to the headland, and
ran until they come there that is now called Þrælaskriða
[‘Thralls’ scree, landslip’].

> Þar fengu þeir Þórarinn tekið Nagla því að hann var nálega
> sprunginn af mæði en þrælarnir hljópu þar fyrir ofan og
> fram af höfðanum og týndust sem von var því að höfðinn er
> svo hár að allt hefir bana það sem þar fer ofan.

> They, Thorarinn (and the men) were able to catch Nagli
> because he was near to die from exhaustion but the thrall
> jumped down there from the cape and perished as was
> expected because the cape was so high that all have death
> who go down there.

> There they, Thorarinn (and co.) were able to catch Nagli
> because he was nearly dead from exhaustion but the thralls
> leaped down there and from off the headland and perished
> as was expected because the headland was so high that all
> have death (from) it who go down from there.

There Þórarin & Co. were able to catch Nagli, because he was
nearly dead of exhaustion [esp. shortness of breath], but
the thralls ran above there and off the headland and died,
as was to be expected, for the headland is so high that
everything dies that falls there.

> Síðan fóru þeir Þórarinn heim og var Geirríður í dyrum og
> spyr þá hve farist hefir.

> Then they, Thorarinn (and the men), went home, and
> Geirridur was at the door and then asks how has perished.

> Afterwards they, Thorarinn (and company) go home and
> Gerrid was in the doorway and asks then what has happened.

Afterwards Þórarin & Co. went home, and Geirríð was in the
doorway and asks them what has happened.

And now for a bonus, here's the first of the two vísur that
are coming up; it's actually one of the easier ones that
I've seen.

Þórarin then spoke (this) vísu:

Varþak mik, þars myrðir
morðfárs vega þorði,
(hlaut örn af nai [nái] neyta
nýjum) kvenna frýju;
barkak vægð at vígi
valnaðrs í styr þaðra,
(mælek hól) fyr hœli
hjaldrs goðs af því (sjaldan).

I guard myself, there where murderer/destroyer
of murder-harm dared to fight
(allotted was the eagle to feed on corpses
fresh), against women’s reproaches [of cowardice];
I bore not mercy in battle
in corpse-adder’ tumult there,
(I speak boasts) for praiser
of din’s god therefore (seldom).

A more normal word-order, courtesy of the editor of another
edition:

Ek varða mik kvenna frýju, þar es myrðir morðfárs þorði
vega (örn hlaut neyta af nýjum nai [nái]); bar-ek-ak af
því vægð at vígi fyr hœli hjaldrs goðs þaðra í valnaðrs
styr – ek mæli sjaldan hól.

I guard myself against women’s reproach (of cowardice),
there where murder-harm’s [= sword’s] murderer/destroyer [=
warrior, here Þorbjörn] dared to fight ((the) eagle was
allotted to eat of fresh corpses); I did not bear,
therefore, mercy in battle for din’s [= battle’s] god’s [=
Óðin’s] praiser there in corpse-adder’s [= sword’s] tumult
[= battle] – I seldom speak boasts.

<Valnaðr> is <val-naðr>, from <valr> ‘the slain’ and <naðr>
'an adder'.

Brian