An alignment problem would not cause a vibration unless the alignment has worn the tires badly, therefore the tires would cause the vibration. If the tires are okay, have the drive axles checked, because a worn drive axle can cause vibration.
The car pulling to the right when the steering wheel is released is most likely an alignment problem, but could also be a "radial tire pull". Normally a rotation will correct that.
An alignment problem will NOT cause your wheels to bend. Normally, only an impact could cause that -- like pot holes, curbs, etc.
this could be due to oil sludge. this is a common problem for 2003 solara. make sure to change your oil often.
Try replacing the tires! Apparently, Solaras suspension is very sensitive to tires with bad belts, bumps, flat spots, etc. Mine was shaking between 40 and 70 mph--replaced the front tires and it's smooth as silk no
try getting your tires balanced
get a wheel alignment
A car's steering wheel will vibrate when driving if the car's alignment needs to be adjusted.
There is no light on the steering wheel.
It is the engine that is vibrating and it is just being felt in the steering wheel. Can be a vacuum leak, or miss in the engine.
Normally it is a tire out of balance. Can also be a bent wheel.
You possibly have warped brake rotors on the front. Or Bad Wheel Bearings.
Adjusting the steering wheel on a 1998 Toyota Corolla is easy. All you have to is find the latch at the bottom and push in to adjust the wheel.
could be a blockage in your fuel lines.
Normally this is caused by a tire out of balance or a bent wheel.
Because the front rotors are warped. You might want to replace the rotors or resurface it.