My 2001 MB E320 vibrates when in drive and at idle. The engine runs fine. It does not vibrate in reverse at idle. What causes this strong vibration?

already check all mounting

check the moter mounts..

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Get a friend to open the hood and look at the engine go up or down in the engine compartment when the brakes are firmly applied and switching between reverse and drive. Look for the motor mounts for behavior where tears exist in the rubber.

Check your throttle body gasket, if it's leaking unmetered air it will idle high, this coupled with a bad ignition coil, plugs not properly gapped or old/worn as well as old/worn spark plug wires will cause a misfire that may not trip the CEL light. Also check your idle air control valve to ensure it's working and clean on the inside of the throttle body.

If the vibration is felt especially when you put the car in drive or when in park if you goose the gas pedal and you feel the whole car vibrate then look to replace the transmission mount. When they weak you can feel a vibration through out the whole car especially when in drive.

check the motor motor mounts for movement,
watch how far engine rocks forward or back with it running and foot on brake

Good afternoon. Sounds like you need to check the engine/transmission mounts. Bad mounts will cause a vibration you are describing and will transmit normal engine vibration into the frame of vehicle causing vibration to occur. Most mounts are made of rubber but some are filled with oil and are called hydro-mounts. Check all mounts for cracked rubber at mount where it attatches to engine,transmission and frame. Hope you find this information useful! Have a great day!

Have your motor mounts checked very soon. This only shows in reverse because reverse causes a backward torque than the engine does in forward gear.

Does it run fine going down the road, Just vibrate at Idle or does it run bad too with a check engine light on?

Check the motor mounts. They might be worn or loose which can cause vibration felt when the engine is reved up or running at higher rpms than at idle.