> að hann höggvi eigi oftar."
> that he doesn't cut more often."

That's the correct literal translation, but the sense of it is "that
he doesn't cut any more" or "that he doesn't cut again" (after this time).

at vitja eigi optarr til Íslands
"never to visit Iceland again"

Nú skaltu verða á bruttu ok koma eigi optarr fyrir augu mér eða í augsýn
"Now be off with you and don't come before my eyes or into my sight
again."

ok leituðu heiðingjar eigi optarr at brenna þá kirkju.
"and the heathens never again tried to burn that church."

Höskuldr verðr við þetta óðr ok kvazk ætla at taka eigi optarr af
honum rán og manntjón
"Hoskuld became furious at this and said he didn't intend to suffer
robbery and loss of men from him again"

Ok er nú þat satt at segja, at vér munum skiljask, ok mun þá betr
hvárratveggju handar, at þér komið eigi optarr mik at hitta.
"And it's now true to say that we will part, and it will be better for
each of us for you not to come to meet me again"

(It can be used, as in this last example, where the event that is not
to be repeated has only happened once.)