My 1995 Olds 88 shakes and has a pretty bad vibration when the car gets up to about 55 MPH and drops down into overdrive. I was wondering if this is a transmission issue or perhaps motor mounts gone bad.

Hello Cransbottom.
The most likely issue here is a misfire.
When your car is at this speed and in overdrive it requires the most power from the ignition coil to jump the gap at the spark plug.
This is because the fuel mixture is very lean and the engine is putting out lots of torque.
The spark is jumping off at the weakest point rather than jumping the gap at the spark plug.
It could be at the ignition coil, a bad ignition wire or the spark plugs.
Remove the spark plugs and look carefully on the white insulator for black/brown streaks down the side. If there are traces, replace the spark plugs and the ignition wires. The wires will be burned on the inside of the boot and the spark will track down there as well.
This is called carbon tracking.
This will also occur on the ignition coils but is more rare.
I have fixed many of these cars with the same symptom as you are experiencing and I believe you should begin with that.

KL