It's vav across many, if not most, Jewish ethnicities (not sure why you'd single out ashkenazi Jews) as well as predominantly a 'v' sound in almost all cases. I googled it and found that waw is accurate if we were talking about semitic origins of the letter, not its modern usage in Hebrew.

Adonai, Elohim, and El Shaddai. All 3 names are used in the Torah and all 3 are plural. We were taught that the God of Israel was one of many gods, but that the ancient Israelites were specifically chosen by this god. This god liked to war with the chosen people of other gods and the Torah is full of those tales. Basically, I'm not talking about kaballah but the authors of the Torah using multiple words for the name of God, some of which being plural.

Vav is a product of ashkenaszi pronunciations due to yiddish. Originally it's Waw.

Vav has nothing to do with Yiddish.

The pronunciation shift occurred in a large number of groups that didn't speak Yiddish, and shifts like that also aren't uncommon cross-linguistically.

The exact same shift happened in Italian, as well: v in classical Latin made a w sound, but morphed to a v in most romance languages.

Pronunciation shifts don't have to come out of influence of other languages, they just kinda happen normally on their own. Sometimes this causes spelling changes (such as the many Spanish words with an h that came from a Latin f, like hablo or hijo), other times it changes the sound of the letter, such as how the Greek phi went from an aspirated p to an f sound, or a j went from a y sound to an English j.

And the multiple names for God thing comes from Kaballah

Kabbalah talks about the multiple names of god, but the Torah itself uses a number of different names for god.

For that matter, look at Hebrew names. You have names like Matityahu (gift of god), Daniel (god is my judge), and eliyahu (god is my god), using different names of god. Why do biblical Hebrew names use both el and yahu to refer to god, if multiple names was a kabbalistic innovation?