Here's my translation. There were a few lines where I could not fully unravel the syntax/grammar so I will be looking for assistance once all translations are in.

Alysseann

177. En við þann átrúnað, at ekki verði at þeim mõnnum,
But, with that belief that nothing (used as a pronoun?) becomes of those men

er heitstrengingar fella á sik,
who draw down curse on themselves for breaking solemn vows,

þá hljóp hann af baki til hans ok hjó hann banahõgg.
then he leapt off the back of his (horse) and struck him (Einar)(acc) a death-blow.

Eptir þat ríðr hann heim við svá búit á Aðalból ok segir þessi tíðendi.
After that he rides home, with such accomplished (ie without further ado) to Aðalból and says (reports) this news (tiding).

Síðan lét hann fara annan mann til smala í selit.
Then he caused (ordered) another man to go to (the) sheep at the shieling.

En hann lét fœra Einar vestr á hallinn frá selinu
But he caused to bring (had brought) Einar onto the slope west from the shieling

ok reisti võrðu hjá dysinni. Þetta er kõlluð Einarsvarða,
and raised a cairn alongside the grave. This is called Einar’s cairn,

ok er þaðan haldinn miðr aptann frá selinu.
and mid evening is marked from there from the shieling (ie when the sun passes over the cairn, when viewed from the shieling, it is considered mid-evening).

Þorbjõrn spyrr yfir á Hól víg Einars, sonar síns.
Þorbjõrn, at Hól, asks (learns) about his son Einar’s slaying [is ‘yfir’ connected with spyrja or a preposition?].

Hann kunni illa tíðendum þessum.
He thinks badly (is greatly displeased) about these tidings.

Nú tekr hann hest sinn ok ríðr yfir á Aðalból
Now he takes his horse and rides over to Aðalból

ok beiðir Hrafnkel bóta fyrir víg sonar síns.
and asks Hrafnkel (acc) for compensations (gen pl) for his son’s slaying.

Hann kvazk fleiri menn hafa drepit en þenna einn.
He (Hrafnkel) declared himself to have (that he had) killed more men than this one.

'Er þér þat eigi ókunnigt, at ek vil engan mann fé bœta,
’To you that is not unknown, that I want to compensate no man with property,

ok verða menn þat þó svá gõrt at hafa.
And men are to have done with that even so (?? I can’t unravel the syntax of this but suspect the sense is “and men will just have to have to accept this.”)

En þó læt ek svá sem mér þykki
But still, I allow (admit) such as seems to me

þetta verk mitt í verra lagi víga þeira, er ek hefi unnit.
this deed of mine (to be) in the worse layer (order of magnitude) of those slayings which I have committed.

Hefir þú verit nábúi minn langa stund,
You have been my neighbour a long time,

ok hefir mér líkat vel til þín ok hvárum okkar til annars.
And (it) has been well pleasing to me towards you, and to each of us towards the other.

Mundi okkr Einari ekki hafa annat smátt til orðit,
(There) would not have become another small (matter??) between us, Einar (and myself),

ef hann hefði eigi riðit hestinum.
if he had not ridden the horse.

En vit munum opt þess iðrask, er vit erum of málgir,
but we two will often repent of this, when we two are too free of speech,

ok sjaldnar mundum vit þessa iðrask,
and more seldom (less often) would we two repent of this,

þó at vit mæltim færa en fleira.
even though we two spoke less (about it) rather than more.

Mun ek þat nú sýna, at mér þykkir
I will now show that, that (it) seems to me

þetta verk mitt verra en õnnur þau, er ek hefi unnit.
this deed of mine (to be) worse than those others which I have committed.

Ek vil birgja bú þitt með málnytu í sumar, en slátrum í haust.
I want to supply your farm with milch cows in summer, and with meat in autumn.

Svá vil ek gera við þik hvert misseri, meðan þú vilt búa.
I want to do such with you each season, while you want to dwell/remain (here).

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