Though both of these terms come from other languages, they are both said in English, depending on where one is. One (ay wey as a more English form) can mean holy crap!, and the other can mean something similar. Maybe it can be due to a related background?
There are a lot of interesting issues here that all sort of are independent but related.
'Oy vey' (pronounced /oj ve/) is an expression of exasperation. It is a shortening of (and loanphrase from) Yiddish: 'Oy weh is mir' = "Oh woe is me", "it pains me" ('weh' is cognate with English 'woe'). Yiddish is a common source of loanwords into English, more common in areas of Ashkenazi Jewish immigration in the US and UK. For example, you start to pour from a carton of milk on your cereal and only a dribble comes out. 'How annoying' or 'Oy vey' is an appropriate reaction. It is often shortened to 'Oy' (which is not to be confused with the BrE or Cockney 'Oy!' which is used to get someones attention and is just a phonologically altered 'Hey!'). Syntactically it is just an interjection in English.
'Ay güey' (pronounced /aj we/ or /aj ɣwe/) is a common phrase in Mexican Spanish. It seems to have been established that 'güey' comes from 'buey' which is from Latin 'bos' for cow. It is used as a very mild epithet, a little more spicy than just AmE 'pal' and 'buddy', or BrE 'mate'. Mexican Spanish is a common source of loanwords into English ('buckaroo' < 'vaquero', 'hoosegow' < 'juzgado').
(note: I am very unsure of its use in English (or Spanish) - I've never heard it as such but that doesn't mean English speakers don't use it especially in a geographical area with lots of Mexican Spanish speakers)
So they are not likely to be related in anyway. Surely there are transplants from Northern New Jersey to Texas (and vice versa) who might use both, but despite their superficial phonological and syntactic similarities, they are not used the same way and are not related in provenance.