halvay is the form used in spoken Hebrew. don't use levay, it's grammatically correct for the meaning 'I wish' ,but it's not used.
By the way, you should in fact say halvay without a vowel after the l, but in colloquial speech they are equally good. The spelling (for both pronunciations) is: הלוואי
The word levay has other meanings than the 'I wish' meaning. One is in grammar and it means 'modifier', and the other means 'after', or 'something that comes along with', as in aftertaste (טעם לוואי), aftereffect (תופעת לוואי). In this meaning the word always comes as a second word of a phrase, as in the examples I gave.
Perheps these other meanings are the reason for the exclusion of this word from 'I wish' contexts (In spoken Hebrew).
If I understand correctly הלוואי means both "I hope" (for the future) and "I wish" (something that regrettably didn't happen).
If someone ask you "Will you come to my birthday party?" and you answer הלוואי, does it mean "I wish I could come but it is not possible", or "I hope so"?