This is purely anecdotal and personal, but I think it tallies quite well with many types of ‘generic broadcast American’ (if there is such a thing).
I would pronounce yeah as @tchrist describes in his comment, with a diphthong /jɛə/. It is the neutral, spoken variant of ‘yes’, which I rarely say in colloquial speech (except for emphasis).
Yeh /jɛ(ː)/ exists for me, but it’s not something I would use often. When I do, I’d quite likely also nasalise the vowel, making it /jɛ̃/. It is a different word to me (well, no, not a different word, but it’s not quite interchangeable with yeah), but I cannot for the life of me think of a conditioning that would cause me to use yeh over yeah.
Yah /jæ(ː)/ is definitely different to me. The difference between yes/yeah and yah is the same as that between no and nah: it’s less definite, more hesitant, and gives more of a feeling that you’ve kind of thought about this for a bit, and on the whole you’ve come to the perhaps not rock-steady decision that, “Sure, why not?”.