Some more information on this. The verb 'breyta' means "act, behave"
or "change". In the modern language 'breytni' is "conduct",
'breyting' "change", but in Old Icelandic, 'breytni' can also
sometimes have the meaning "change". As we were having some
difficulty with this word, I consulted Eysteinn Björnsson. His reply:

"Synonyms of breytni = hegðun (behaviour), framferði (conduct). The
meaning can also pass into viðleitni (endeavour) which it somewhat
does here."

"So, what she is saying, i.e. "höfum við bæði breytni til þess á alla
vega" is equivalent to "both of us conduct ourselves towards that end
in all (possible) ways". She is saying that they both behave in the
proper manner designed to achieve sexual satisfaction, that it is not
for want of trying. Adding the idea of viðleitni to the mix, "hafa
breytni til e-s" almost means "strive in one's conduct towards
something", and in certain cases it could go so far as to mean
"employ all possible tricks in the attempt to reach the goal".

Hence the example I found from the 1001 Nights:

>En stúlkan var ekki til annars komin en að æsa í honum
>losta, og hafði hún breytni til þess á marga vegu.

EB: "Here the meaning passes all the way into "tricks", as in the
"tricks" employed by a whore to produce lust. But the basic meaning is
still only "behaviour, conduct, acts" - it just gets variously
coloured by the context. Here the lady "commits various acts with a
certain purpose in mind".