Here´s my translation

Alan

Nú er að segja frá ferð Kolfinns. Hann var sár mjög sem sagt var. Ár stórar
Now (one) is to say about Kolfinnr‘s journey. He was very wounded (sore) as was said. Large rivers (fem plural forms)

voru á leið hans. En er hann kom af Leiruvogsá þá gerði honum kalt mjög og
were on his way (in his path). But when he came from (out-of, af, Z.i.2) Leiruvogsá (Clay-Creek-River) then (it) became for him very cold (ie he became cold) and

stirðnaði hann. Frost var á nokkuð.
he became-stiff (presumably from the cold, stirðna, Z1). A frost was on (see á, Z.iii.7, I suspect in the sense of „lying on the ground“) somewhat.

Maður hét Korpúlfur. Hann bjó á Korpúlfsstöðum. Hann var gamall maður og
(There) was a person (man) called Korpúlfr. He lived at Korpúlfsstaðir. He was an old person (man) and

kallaður heldur forn í brögðum. Son átti hann þann er Grímur hét. Hann var
called rather ancient (as distinct from merely old?) in looks. He had that son who was-called Grímr. He was

ungur og frálegt mannsefni. Korpúlfur var móðurbróðir Kolfinns.
young and quickly („in no time at all“,  neut sg ending suggests adverbial use) (was) a man (person)-of-promise. Korpúlfr was Kolfinnr‘s mother‘s-brother (maternal uncle).

Þangað sneri Kolfinnur sinni ferð og fékk þar góðar viðtökur. Batt Korpúlfur sár hans.
Kolfinnr turned his journey thither and got there good hospitality (plural of viðtaka, see Z2). Korpúlfr bound his wounds.

Dvaldist Kolfinnur þar um hríð en sendi móður sinni orð hvað hann dvaldi.
Kolfinnr stayed there a while but sent his mother word what delayed (dvelja, Z1) him (masc acc sg here).

Þenna sama morgun sem Örn var veginn kom Esja snemma til fóstra síns. Hann
This same morning as Örn was slain (vega, Z7), Esja came early to her fosterling. He

fagnaði henni vel og spurði að tíðindum.
greeted her well and asked of tidings.

Esja sagði honum víg Arnar austmanns og alla atburði þá er þar urðu: "Nú vil
Esja said to him of (the) man-slaughter of Örn (the) Norwegian (East-man) and all those (masc acc plural of sá) events which happened there:

"Nú vil eg að þú breytir búnaði þínum. Hefi eg hér nú loðkápu er eg vil að þú berir.
“Now I want that you change your dress (attire). I have here now a fur-cloak which I want that you wear (bera, Z2).

Skyrta er hér annað klæði. Það þykir mér líkara að hún slitni ekki skjótt
A shirt is here a second garment. That seems to me more-likely that it (hún because skyrta is a feminine noun) would-break (wear-out, subjunctive present) not speedily

hvorki fyrir vopnum né fyrnsku. Sax er hér hinn þriðji gripur.
neither (hvárgi) for (ie because of) weapons nor age (fyrnska, Z1, or witchcraft, fyrnska, Z2, may be intended here given the supernatural elements of this story).  A short-sword is here the third item-of-value (no superlative here).

Þess væntir mig að það nemi hvergi í höggi stað því að þú munt nú skjótt verða að reyna
(It) gives me hope/expectation of (ie I expect) that it (ie the short-sword) would-stop (subjunctive, nema stað, Z1) not at all in (the) stroke because you will now quickly be-obliged to (verða að + inf) test (try out, reyna, Z1)

hversu þér bíta vopnin."
how the-weapons (neut plural) bite (cut) for you.”

Búi kvað hana ráða skyldu. Búi hélt ferðum sínum í Kollafjörð.
Búi declared her (that she) should have-her-way (decide). Búi steered (directed) his course (journeys) into Kollafjörðr.

Var nú engi þröng á palli hjá Ólöfu. Jafnt lét hún til Búa nú sem fyrr.
No crowd (throng) was now on (the) dais by Ólöf. She behaved (láta, Z7) towards Búi precisely as before.

Þá er Kolfinnur var gróinn sára sinna sagði hann Korpúlfi frænda sínum að
Then when Kolfinnr was healed of his wounds, he said to Korpúlfr, his kinsman, that

hann vill finna móður sína.
he wants to find his mother.

Korpúlfur bað hann því ráða "en því vil eg ráða að þú hafir eigi lengur
Korpúlfr asked him to have-his-way (decide for himself, make up his own mind) in that “but in that I want to advise that you should-wear (see hafa, Z9)  no longer

tötra þessa." sagði Korpúlfur, "vil eg að þú hafir héðan góð klæði og vopn
these tatters (tattered-garments).” Said Korpúlfr, “I want that you wear (hafa, Z9) from-here (ie henceforth) good (neut plural) clothes (neut plural) and weapons (neut plural)

er eg vil gefa þér. Muntu þeirra brátt þurfa. Þar með vil eg gefa þér Grím
which I want to give to you. You will have-need of them soon. Therewith (ie in addition to these), I want to give you Grímr,

son minn til fylgdar og föruneytis."
my son, for support and company.”

Kolfinnur kvað svo vera skyldu.
Kolfinnr declared (it) should be so.

Eftir það fóru þeir frændur til Vatns að finna Þorgerði. Varð hún þeim fegin
After that those kinsmen journeyed to Vatn to meet (find) Þorgerðr. She was glad of them (ie their coming)

og spurði hvað Kolfinnur vildi að hafast.
and asked what Kolfinnr wanted to do.