I know that the English "always" comes literally from "all ways". the Bavarian "oivai" sounds almost the same, means the same, but doesn't seem to be as straight forward. While "oi" means "all" and "oiss" means "everything", "vai" has no meaning (well, it means "woman" or "wife", but I don't think that's related). The modern Bavarian word for "way" is "veeg", which could possibly be a recent adaption from the German "Weg". This seems to be unlikely though if you compare similar words to "-vai" such as Bavarian "mai" and German "maul" (Meaning "mouth" in English, but is offensive in German).
One interesting theory I read (I don't remember where) is that it comes from the Latin "aliubei" (meaning "sometimes"), which could make sense, but it would be a huge coincidence.
edit: Some alternative ways to write "oivai" are "o-i/ll-[a]-v/w-a/e-i-[s]". I just took the one that is closest to being phonetic.