Here’s my translation

Alan

Gríðr mælti þá mjök reiðuliga: "Heyr þú, vándr herjansson, hví hugðir þú ek munda þola, at þú blygðaðir dóttur mína? 
Gríðr spoke then very angrily: “Hear-you, wicked brat (lit: son of Herjan, Lord of Hosts), why would you think [that] I would endure, that you would-seduce my daughter?

Nei," segir hún, "þú skalt fá dauðann í stað." 
No,” says she, “you shell receive the-death in stead (or possibly, ‘at once’, ‘on the spot,’ see <staðr>, Z2).”

Illugi mælti þá: "Mitt hjarta hefir aldri hrætt orðit, ok því kom ek í helli þinn, at örlögin hafa svá fyrir ætlat. 
Illugi spoke then: “My heart has never become (been) afraid, and I came into your cave for that [reason], that (<því … at>) the-fates have pre-ordained [it].

Þó deyr engi optar en um sinn, ok því hræðumst ek ekki þínar ógnir." 
Still no-one dies more-often than once, and for that [reason] I fear not your threats.”

Við þessi hans orð kastar Gríðr honum aptr. 
With these words of his Gríðr casts him back.

Hann snerist þá at brúði sinni ok var þá allglaðr. 
He turned-himself then towards his ‘bride’ and [he] was then extremely-happy (masc nom sg).

Ok er hann var sem blíðastr við hana, vefr Gríðr hár hans um hönd sér ok kippir honum á stokkinn fram ok reiðir saxit allt at höfði honum: "Djarfr ertu, ok nú í stað skaltu dauðann fá."
And when he was as agreeable-as-possible (see <sem>, Z3) towards her (the daughter), Gríðr wraps his hair around her hand and draws him forward onto the-board-at-the-front-of-the-bed and brandishes the-short-single-edge-sword completely at his head: “You are impudent, and now in-stead (or possibly, ‘at once’, see <staðr>, Z2) you-shall receive the-death.”

En Illugi sagðist eigi hræðast dauða sinn. 
But Illugi said-of-himself not to-fear his death.

Hún mælti þá hlæjandi: "Engan hefi ek slíkan hitt, at eigi hafi hræðzt dauða sinn, nema þik. 
She spoke then laughing: “I have met no-one such (similar), that has not feared his death, except you.

Far þú nú til svefns ok sof vel!" 
Go you now to sleep and sleep well!’

Ferr Illugi nú ok snýst at konu sinni ok er nú allra blíðastr við hana. 
Illugi goes now and turns-himself towards his wife and [he] is now all the more agreeable (lit: most-agreeable of all, see <allr>, Z6, <blíðastr> is masc nom sg) towards her.

Gríðr hleypr þá enn at sænginni ok kippir honum fram á stokkinn. 
Gríðr leaps then yet (again) at the-bed and draws him forward onto the-board-at-the-front-of-the-bed

Hún reiðir nú saxit, ok mjök er hún ófrýnlig at sjá, en allt fór sem fyrr, at Illugi kvaðst eigi hræðast. 
She brandishes now the-short-single-edges-sword, and she is very unpleasant-looking to see (behold), but everything went as before, that Illugi declared-of-himself not to-be-afraid.

Gríðr mælti þá: "Eigi ertu sem aðrir menn, þínar æðar skelfast hvergi, ok þú hræðist ekki. 
Gríðr spoke then: “You are not like other persons (men), your veins tremble-with-fear not-at-all, and you fear not.

Nú skaltu þiggja líf af mér, ok þar með gef ek þér dóttur mína, er Hildr heitir, ok fæ ek þó aldri launat þinn velgerning, því at þú hefir komit mér ór miklum álögum, því at með slíkum hætti hefi ek margan myrt ok drepit, ok hafa allir hræðzt mitt it ógurliga sax. 
Now you shall receive life from me (ie I will spare you), and there-with I give you my daughter, who is-called Hildr, and yet I am never able to reward (<fæ launat>, <fá> + pp, Z7) your goodness (well-doing), because you have brought me (<kóma> + dat, Z3) out-of great tribulations (or spells <álag>, Z2 or Z4), because with such a way (ie in like manner) I have murdered and killed many, and all have feared the terrible short-single-edged sword of mine.

Sextán vaska menn hefi ek drepit með þessu saxi, ok væri slíkt þó eigi kvenna verk. 
Sixteen valiant persons (men) have I killed with this short-single-edged sword, and such should-be nevertheless not women’s work.

Nú mun ek segja þér ævisögu mína, en þú hlýða:
Now I will say to you my life-story, but (and) you [will] (from  preceeding <mun>) listen (infinitive)

5. Saga Gríðar
5. [The] story of Gríðr

"Konungr sá réð fyrir Álfheimum, er Áli hét. 
“That king ruled over Álfheimar (Elf-Abodes), who was-called Áli

Hann átti sér drottningu, er Álfrún hét. 
He had for himself a queen, who was-called Álfrún.

Þau áttu dóttur eina, sú hét Signý. 
They had a daughter only, that-one (ie she) was-called Signý.

Hún var at öllu vel at sér.
She was in all respects well with-regard to herself (highly accomplished)