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.
A worn out Universal joint in the rear driveshaft.
If your car shakes while accelerating check your motor mounts. Then check your transmission.
Exhaust fumes may enter and that is not good.
You have no wheels. - Geoff
Slow engine RPM is the main reason a car may be sluggish while accelerating. However, it also could be due to the oil.
I just fixed this problem on my own car, and it was that the rubber part on both the right side motor mounts was broken, so it would shake and make a loud noise when in drive and especially while accelerating. Depending on your car, you might be able to check for yourself, at least on a top side mount.