http://www.usask.ca/english/icelanders/proverbs_BNS.html

'eigi' = present subjunctive 3rd person plural of the verb 'eiga'.
'ýmsir' = masculine nominative plural of the adjective 'ýmiss'.
Is 'högg' singular or plural? I'm not sure.

So maybe something like:

"...that each side alternately will have a blow/strike/cut in the house"
"...that each [of us] by turns will suffer a blow to their household"
"...that there will be blows struck on either side"

How much is the idea of alternation explicit; or does 'ýmsir' just
mean "either side"?

LN