Sounds like it needs an overhaul.
Poor oil pressure can be due to worn main & rod bearings and the shaking with failure to start means low or no compression which can be worn valves and/or worn piston rings.
Just sounds like it needs a new motor.
Also could be a broken timing chain which means the valves aren't being moved and the cam isn't turning so the oil pump isn't being driven.
Sorry, sounds bad.
Most likely warped rotors
If a 2001 Cadillac DeVille shakes when the car is idle, there could be an issue with the powertrain. There could also be a problem with the crankshaft position sensor.
I'm having the same problem right now, its my rear rotors. They are warped from the pads heating them to too high of temp. Hope this helps.
It is a piece of Junk
Start checking out your engine and transmission mounts. Check the rubber to make sure it isn't torn.
Replace engine cushions
The Vehicle shakes because of the virbration produced by the engine at the stop sing
engine rubber mounts or timin out
That's a misfire-ah....
Engine miss.
An automobile engine usually shakes when it is being revved due the crank rotation. When revved in neutral, a torque is produced due to the reaction of the motor.
My Honda civic 2002 shakes fora few seconds as I turn the engine off.It happened right after replacing the engine mount on the driver's side.