Heil Erla!

> I've done a rather worse job than usual, partly from haste,
> and partly because I was hitting expressions that I couldn't
> quite make sense out of. So this translation is litteral enough
> that it doesn't properly make clear what was meant in some places.

It's not that bad - though it does feel slightly rushed.

> Þorlákr beiddi Þránd eftir skiptit at hann mundi
> hafa heimabólit,
> Þorlákr asked Þrándr after the division to let him
> have the homestead

Correct.

> en hann lausafé meira, en Þrándr vildi þat eigi.
> and he (would have) more moveable property, but
> Þrándr didn't want that (it).

Correct.

> Fór Þorlákr þá í burt ok fekk sér annan bústað þar í eyjunum.
> Þorlákr then went away and got himself another dwelling-place
> there in the islands.

Correct.

> Þrándr seldi á leigu landit í Götu mörgum mönnum ok
> tók leigu sem mesta,
> Þrándr rented out (sold at rent) the land at Göti
> (to) many people and took as much rent as possible
> [this is a guess; litteral looks like "as most rent"],

Correct. The name is 'Gata', though.

nom. Gata
acc. Götu
dat. Götu
gen. Götu

> en hann réðsk til skips um sumarit ok hafði lítinn kaupeyri
> and he hired? [for] a ship in the summer and had few (little)
> trade goods.

Middle voice! :-) The meaning of the verb refers back
to the subject. He hired _himself_ to a ship.

> ok fór til Noregs ok hafði boejarsetu um vetrinn ok þótti
> jafnan myrkr í skapi.
> and he went to Norway and had a dwelling there through the
> winter and seemed equal darkness in disposition. [was his
> temper as dark as the Scandinavian winter ... i.e. very
> dark ... i.e. depressed and/or angry and/or ???]

'Jafnan' is an adverb meaning "always".

> Þá réð fyrir Noregi Haraldr gráfeldr.
> Then he went before Harald Greyskin of Norway.

The phrasal verb 'ráða fyrir' means "rule over".

> Um sumarit eftir fór Þrándr með byrðingsmönnum suðr
> til Danmerkr
> In the next summer Þrándr went south to Denmark with
> merchant seamen

Correct.

> ok kom á Haleyri um sumarit.
> and came to Haleyr in the summer.

Correct. It's 'Haleyrr', though.

> Þar var þá fjölmenni sem mest,
> There was then a crowd of men as most [presumably
> a really big crowd, perhaps as big as any],

Yes! I like that, "as big as any".

> ok svá er sagt,
> and he said thus,

This shouldn't be so difficult, it's exactly like
the English construction.

ok svá er sagt
and so is said

> at þar kømr mest fjölmenni hingat á Norðurlönd meðan
> stendr markaðrinn.
> that in that place came the biggest crowd of people
> hither to Northland when the market stands.

More or less. Note, though, that 'lönd' is in plural
and that 'kømr' is in present tense.

> Þá réð fyrir Danmörk Haraldr konungr Gormsson er
> kallaðr var blátönn.
> Then he went before Harald Gorm's son, king of
> Denmark, who was called blue tooth.

Again 'ráða fyrir' occurs.

> Haraldr konungr var á Haleyri um sumarit ok fjölmenni
> mikit með hánum.
> King Harald went to Haleyr in the summer and a great
> crowd of people with him.

If we stay literal it's "was at Haleyrr"..

Kveðja,
Haukur