Here’s my translation

Alan

Hann varð skjótari til að svara en Hrefna: "Ekki skal hún falda sér með
He needed (ie felt compelled, verða + inf, Z7,or is it simply “happened” here?) to answer more-quickly than Hrefna: “She shall not array herself with

motri að þessu boði því að meira þykir mér skipta að Hrefna eigi hina mestu
(the) head-dress at this feast because (it) seems to me to be of more importance (see skipta, Z4) that Hrefna possess the greatest

gersemi heldur en boðsmenn hafi nú augnagaman af að sinni."
treasure rather than guests (lit: feast-persons) have now a visual-treat (lit: eyes’-enjoyment) from (it) at the present time (sinn).”

Viku skyldi haustboð vera að Ólafs. Annan dag eftir ræddi Guðrún í hljóði
(The) autumn-feast should last (vera, Z3)a week at Ólafr’s. The next day after, Guðrun spoke on the quiet

til Hrefnu að hún skyldi sýna henni moturinn. Hún kvað svo vera skyldu.
to Hrefna that she should show her (Guðrún) the-head-dress. She declared (it) should be so.

Um daginn eftir ganga þær í útibúr það er gripirnir voru í. Lauk Hrefna upp
During the day after they walk to that store-house in which the-valuable-items were. Hrefna opened up

kistu og tók þar upp guðvefjarpoka en úr pokanum tók hún moturinn og sýndi
a chest and took there-up a bag-of-guðvefr (a costly fabric, velvet) but (and) out-of the-bag she took the-head-dress and showed (it)

Guðrúnu. Hún rakti moturinn og leit á um hríð og ræddi hvorki um löst né lof.
to Guðrún. She unfolded (rekja) the-head-dress and looked on (it) for a while and spoke about neither fault nor praise (she neither faulted nor praised it).

Síðan hirti Hrefna moturinn og gengu þær til sætis síns.
After-that Hrefna concealed (hirða, Z3, MnI spelling) the-head-dress and they walked to their seat.

Eftir það fór þar fram gleði og skemmtan.
After that merriment and amusement ensued (took place, lit: went forward, fara fram. Z18)) there.

En þann dag er boðsmenn skyldu í brott ríða gekk Kjartan mjög um sýslur að
But (And) on that day when (the) guests should ride away, Kjartan went much about (the) business (ie went about as an overseer, see sýsla, Z1) to

annast mönnum hestaskipti, þeim er langt voru að komnir, og slíkan
take-care of changes-of-horses for (the) people, those who were (had) come a-long-way, and such

fararbeina hverjum sem hafa þurfti. Ekki hafði Kjartan haft sverðið
furthering-the-journey (travel arrangements, provisions for the journey) for everyone who (whosoever) has needed (it). Kjartan had not had the-sword

konungsnaut í hendi þá er hann hafði að þessu gengið en þó var hann sjaldan
“King’s-gift” in hand when he had gone to this (ie attending to the travellers) but nevertheless he was seldom

vanur að láta það hendi firr ganga. Síðan gekk hann til rúms síns þar sem
accustomed to allow that (ie the sword) to go far (=fjarri) from hand. After-that he walked to his seat (bed, place, room, not sure which but obviously that spot where he was immediately before he started helping out) where

sverðið hafði verið og var þá á brottu. Hann gekk þegar að segja föður sínum þessa svipan.
the-sword had been and (it) was then away (ie missing). He walked at-once to say (report) this sweeping (swiping, theft? sudden loss? fem acc sg of svipan = svipr?,) to his father.


Ólafur mælti: "Hér skulum vér fara með sem hljóðast og mun eg fá menn til njósnar
Ólafr spoke: “We shall go herewith as silently (quietly, covertly) as possible and I will get people (men) for scouting (covert surveillance activities, note: noun)

í hvern flokk þeirra er á brott ríða."
in each party-of-men (masc acc sg) of those which ride away.”

Og svo gerði hann.
And so he did.

Án hinn hvíti skyldi ríða með liði Ósvífurs og hugleiða afhvarf manna eða
Án the White should (ie was to) ride with Ósvífr’s party and pay-attention-to (infinitive) (the) strayings of persons (gen pl) (men, ie deviants J) or

dvalar. Þeir riðu inn hjá Ljárskógum og hjá bæjum þeim er í Skógum heita og
(their) stops (tarryings). They ride in by Ljárskogur (Forests of new-mown-grass (gen sg of ljá)? Not a very tall forest, apparentlyJ) and by those farms (dat plural) which are-called in-Skogur (Forests) and

dvöldust hjá skóginum og stigu þar af baki. Þórólfur son Ósvífurs fór af
made-a-stay by the-forest (dat sg) and dismounted (stepped off (horse) back) there. Þórólfr, son of Ósvífr went from

bænum og nokkurir aðrir menn með honum. Þeir hurfu í brott í hrískjörr nokkur
the farm (dat sg) and some other persons (men) with him. They disappeared (see hverfa, Z2) into some brushwood

á meðan þeir dvöldust hjá skóginum. Án fylgdi þeim til Laxár er
while they (ie the main party) stayed by the-forest. Án accompanied them to Laxá (Salmon-River) (so as not to arouse suspicion, presumably) which

fellur úr Sælingsdal og kvaðst hann þá mundu aftur hverfa.
flows (falla, Z4) out-of Sælingsdalr (Wealthy-man’s-dale) and he declared-of-himself then (that he) would turn back.

Eigi taldi Þórólfur mein á því þótt hann hefði hvergi farið. Þá nótt áður hafði fallið lítil snæfölva
Þórólfr reckoned (there to be) not harm in that, even-if he (ie Án) had travelled not-at-all (ie he didn´t see the point of Án’s coming along for the ride –and this was just as Án would want it). The night before (ie the previous night) a little thin-cover-of-snow had fallen

svo að sporrækt var. Án reið aftur til skógar og rakti spor Þórólfs
so that (it) was possible-to-trace-footprints. Án rode back (aptr, not eptir) to (the) forest and tracked (the) footprints of Þórólfr

til keldu einnar eða fens. Hann þreifar þar í niður og greip á sverðshjöltum.
to a certain bog or fen (quagmire). He feels-with-his-hand there-in down and seized onto sword-hilts.