96 Pontiac Acting Odd

She ticks like a time bomb, the faster she goes, the more it ticks.
Over 70mph it begins to shake a bit.
The check oil light refuses to go off, even through there is oil in there.

Also, how can you tell if the transmission is on the fritz?

The check oil light isn't for low oil, it's for low oil pressure. The ticking is likely from the lack of oil pressure to fill the lifters. If indeed you have low oil pressure, you are slowly (or quickly) running the risk of destroying your engine. While I haven't done it myself, I've heard that replacing the oil pump isn't all too difficult.

The shaking at 70+mph, may be a slight out of balance tire. If it was engine related, it would shake more at a certain RPM, not wheel speed.

And there are many different ways for a transmission to go south. Poor shifting, not shifting, soft shift, grinding, etc. You are going to have to be more specific as to what it's doing.