In an informal setting, where it is being used to agree, affirm, or in the place of the word yes, yeah is the more modern, preferred, and commonly used version. If it is being used in a more formal setting, like a job interview, the formal yes would be the more appropriate choice over yea or yeah.
Yay. Yay is an exclamation that shows feelings such as excitement, joy, happiness, triumph, and approval. The origin is fuzzy though. opens in a new window Some dictionaries say it came from yeah, but most seem to think it evolved from the adverbial yay in the phrases yay big and yay high, but then the opens in a new window Oxford English Dictionary says that the yay in yay high probably came 1ttRgC.