How can I tell if the tea has been stored properly, is not too stale or oxidized?
You can't (or at least I can't) tell without a lot of experience with teas of that sort.  Generally, a sufficiently fresh tea will have a decently strong fragrance when you smell the dry leaves.  As it grows stale, the fragrance will be replaced gradually by mustiness.  But which fragrance to expect varies dramatically by the tea.  For instance, pan-fried greens like dragonwell (longjing) tend to smell vaguely nutty, while a sencha will smell more grassy.  Dragonwell will also be more yellowish while the sencha will be more greenish.  But these are two of many different varieties of green.

Also, there's a continuum of oxidation from green to black, so "too oxidized" is really a matter of taste.  If you buy a Darjeeling (black), it'll tend to be lightly oxidized for a black tea; if your green is darker than that, maybe it shouldn't be called green.

I'm sure with appropriate analytical chemistry equipment you could determine some aspects of tea "quality"--but this would be complete overkill unless you're running a major tea business and you want to ensure quality.  And even then, you'd probably be better off hiring a number of taste-testers.

There is one test (but it's not definitive): brew the tea, then leave the cup out for a day.  If it doesn't get dramatically darker by the end of the day, it's already mostly oxidized.

In any case, if you like the tea, why do you care so much about the quality?  You can find some outrageously expensive teas--I've noticed some South Korean greens in particular--that start getting into the price ranges of fine wines, but unless you're doing this to impress people, you're better off trying a variety of samples and then getting the one/ones you like.  (Hopefully you won't find that you really like those South Korean greens....)