That's usually caused by a cylinder "misfire", meaning that one or more cylinders are not firing properly.
It can be caused by bad plugs, damaged wires, worn distributor cap, injector problems, burned valves... and the list goes on.
When you are parked or in neutral while the car idles, your engine will shake. The vehicle will also get poor gas milage. Bad gas can also cause engine failure.
Check for a busted engine or tranny mount.
Check all front end components for wear. Then check the engine and transmission mounts as the engine could be shifting and causing the shake.
One possibility is you might have one bad tire or a u-joint.
Your front, left or right axle needs to be replaced.
Maybe its your motor mounts.
If your car shakes while accelerating check your motor mounts. Then check your transmission.
A worn out Universal joint in the rear driveshaft.
You have no wheels. - Geoff
Exhaust fumes may enter and that is not good.
Slow engine RPM is the main reason a car may be sluggish while accelerating. However, it also could be due to the oil.
could be a broken engine mount