Why do my car vibrates and sometimes go off when i try to accelerate or move the car

The vibration my best guess would be tire related carousing an out of balance situation. Visually inspect the tire for bump that may indicate the tire took a hit on a pothole or the like causing the tire to rupture inside , also check between the tires tread for ant cracks again indicating the tire to be coming apart. A bent rim or somesthims the lug nuts may have loosened . If you don't see anything try putting the tire on the front of your car and see if the vibration has now moved to the front of the car if it did I think you have identified the problem , get a new tire .
With your engine starting I would need a little more information in order to help you . Hope this helps . Have a great day

Sounds like you need new engine mounts

Hello,

If problem only occurs 'under power' sounds like a u-joint (driveline - rear wheel drive) or a cv-axle (front wheel drive). Check for excessive play, fluid, boot tear and breakage.

Does it have a vibration when idleing? If it has both, it is most likely the motor mounts. Either way it is a very easy thing to do. Make sure the car is in Park with the e-brake set. Pop the hood and have someone press the accelerator pedal, does the whole engine move (usually in a tilting motion)? If so the motor mounts may be bad.

What year?

bad distributor cap and or ignition wires.

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Check motor mounts.

Check the cable near the abs modulator. Some C180, C200 have short circuit from broken insulators

if your trans fluid is full it may be an internal problem in the gearbox even in the converter its hard to diagnose without seeing the car but i can sure try to help if you can add any other noises or symptoms i will see if i can help you pinpoint the problem