Here is my translation. Comments and suggestions in red, queries underlined.

Kveðja

Alan

Síðan stígur Höskuldur á skip sitt og siglir til hafs. Þeim byrjaði vel og
After-that Höskuldr steps onto (boards) his ship and sails out-to sea. For them (it) blew well (ie they got fair winds) and (they)

komu að fyrir sunnan land, sigldu síðan vestur fyrir Reykjanes og svo fyrir
came to (the) south (of) (the) country, sailed then west round (see fyrir, Z.II.5) Reykjanes (Steam-Ness) and also round

Snæfellsnes og inn í Breiðafjörð. Höskuldur lenti (lenda) í Laxárósi, lætur (láta) þar bera
Snæfellsnes (Snow-Mountainr-Ness) and inside into Breiðafjörðr (Broad Fjord). Höskuldr landed in Láxárós (Salmon-River-Mouth), causes there to carry

farm af skipi sínu en setja upp skipið fyrir innan Laxá og gerir þar hróf að
cargo from his ship but (and) raises (lays) up the-ship inside Laxá (Salmon-River) and makes (builds) there a shed

og sér þar tóftina (can´t find this in Z) sem hann lét gera hrófið. Þar tjaldaði hann búðir og er það kallaður Búðardalur.
and (one) sees there the (remains?) where he had caused to make the-shed. There he pitched (fitted up) booths (with tent roof and hangings) and that is called Búðardalr (Booth-Dale).


Síðan lét Höskuldur flytja heim viðinn og var það hægt því að eigi var löng
After-that Höskuldr caused to convey home the wood and that was easy because (it) was not a long

leið. Ríður Höskuldur eftir það heim við nokkura menn og fær (fá) viðtökur góðar
way. Höskuldr rides after that home with some men (persons) and receives a good reception

sem von (ván)er. Þar hafði og fé vel haldist síðan. Jórunn spyr hver kona sú væri
as is (the) expectation (as is expected). There had also(the) wealth continued (been maintained) since (he left). Jórunn asks who that woman was

er í för var með honum.
who was in company (see för, Z1) with him.


Höskuldur svarar: "Svo mun þér þykja sem eg svari þér skætingu. Eg veit eigi nafn hennar."
Höskuldr answers: “So will (it) seem to you like I answer you (with) a scoff. I know not her name.”


Jórunn mælti: "Það mun tveimur skipta að sá kvittur mun loginn (pp of ljúga) er fyrir mig
Jórunn spoke: ‘That will turn-out in one of two ways (see skipta, Z4) that (1) that loose-rumour will (be) falsely-told  which before me

er kominn eða þú munt hafa talað við hana jafnmargt sem spurt hafa hana að nafni."
is (has) come or (2) you will have spoken with her equally-greatly (enough times) as to have asked her for (her) name.”


Höskuldur kvaðst þess eigi þræta mundu og segir henni hið sanna og bað (biðja) þá
Höskuldr declares-of-himself (that) he would not contradict that and says to her (the) truth and asked that-one (ie her?)

þessi konu virkta og kvað það nær sínu skapi að hún væri heima þar að vistafari.
for tender care of this woman (ie recommended this woman to her special charge, see under virkt, Z1) and declared that near his heart (ie his strong wish) that she were (stay) at-home there in domicile (ie she be part of the household).


Jórunn mælti: "Eigi mun eg deila við frillu þína þá (acc fem sg pronoun) er þú hefir flutt (flytja) af
Jórunn spoke: “I will not quarrel with (see deila við, Z5) your concubine, that-one whom you have conveyed (brought) from

Noregi þótt hún kynni góðra návist en nú þykir mér það allra sýnst (see allr, Z6) ef hún er
Norway even-though she makes-known a friendly presence (?) but (and) now that seems to me all-the-more likely if she is.

bæði dauf og mállaus."
both deaf and speechless (dumb).”


Höskuldur svaf hjá húsfreyju sinni hverja nótt síðan hann kom heim en hann
Höskuldr slept alongside his wife every night after he came home but (and) he

var fár við frilluna. Öllum mönnum var auðsætt stórmennskumót á henni og svo
was cool (see fár, Z2) towards the-concubine. To all men was easily-seen (the) signs (mót) of greatness (stórmennsku)  (ie her nobility or maybe it is her expanding tummy J) in her and also

það að hún var engi afglapi.
that, that she was no fool.


Og á ofanverðum vetri þeim fæddi frilla Höskulds sveinbarn. Síðan var
And in the-latter-part (of) that winter (the) concubine gave-birth-to Höskuldr’s male-child. After-that was

Höskuldur þangað kallaður og var honum sýnt barnið. Sýndist honum sem öðrum
Höskuldr thither called and the-child was shown to him. (It) seemed to him as to others

að hann þóttist eigi séð (sjá) hafa vænna barn né stórmannlegra. Höskuldur var að
that he bethought-himself not to have seen a more-beautiful child nor a grander (one). Höskuldr was 

spurður (pp of spurja) hvað sveinninn skyldi heita. Hann bað sveininn kalla Ólaf því að þá
asked what the-child should be-called. He asked to call the-boy Ólafr because then

hafði Ólafur feilan andast litlu áður, móðurbróðir hans. Ólafur var afbragð
had Ólafr feolan died a little (shortly) before, his mother’s-brother. Ólafr was surpassing

flestra barna. Höskuldur lagði (leggja) ást mikla við sveininn.
most children. Höskuldr laid-out much love towards the-boy.