The following words are NOT the same and they are NOT interchangeable with one another:
Yea means yes. It's the opposite of nay as in: "Do you want to win the lottery? Yea or nay?"
Yay is an interjection of joy as in: "I just won the lottery. Yay for me!"
Yeah also means yes as in: "Did you just win the lottery?" "Yeah, I did."
I say yay for those of you that regularly choose the right one.
Yeah, I did.