Could one use ett sätt instead of en väg
Yes, but only if you mean it like "way to solve [something]".
Får man översätta "peculiar" med "egendomlig" eller "besynnerlig" i detta sammanhang?
Yes, that’s fine.
särskild is more like "particular" in the distinct sense.
Är "särskild" en möjlig översättning för "peculiar" också?
No, not really. Särskild is more about certainty or pointing out a specific one of something. Peculiar is more about something odd.
klart, tack! :)
I think that that you're thinking of the word "particular"
Hon valde ett ovanligt väg.
I'm at a loss here.
väg is an en-word.
It appears 'annorlunda', like 'kul', is one of those adjectives that doesn't change:
en annorlunda väg,
ett annorlunda sätt
Yes - that's actually the rule for all adjectives ending in an unstressed vowel. It's actually not quite true for kul, though - it just usually isn't inflected. But it's a little more complicated than that.