I notice when i shut my solara off, the engine shakes and it transfer to the body resulting in the body shaking but its only for a second what could be the problem? Also when im completely stopped at a redlight i feel vibration through the steering? Any help would be appreciated.

 

Dogbone mount, transmission mount.
If it's trying to continue to run, that normally means it's running hot, ignition timing is too far advanced, or even a possible slow oil leak into the cylinders.

 

Yea, its not trying to run it shuts off fine, just it vibrates the car when it does shut off.