hi it sounds like your universail joints or tail shaft
If it only vibrates when you accelerate than it is most likely a bad axle.
more likely a supension or tire problem, depends on where you're feeling it vibrate.
Most likely warped brake discs
there could be several reasons for this problem the most likely being an alignment problem, if it occurs only when your braking it is probably warped rotors or out of round drums depending on your braking system bad spark plugs or wires
It is very likely you have something wrong with your engine.
Usually when a car makes squealing sound after accelerating with the heater on, the serpentine belt is a little loose. It likely needs adjusting by a professional.
Most likely rotors are "out of round" and need to be either re-surfaced or replaced.
If it only vibrates at idle in gear it more than likely has a severe vacuum leak. Can also be a broken engine or transmission mount.
check tire balance. check tire for seperation. loose steering or suspension parts.tire problem most likely.
It could be your motor mounts (usually always slightly vibrating the car, especially when accelerating) or most likely not aligned/damaged driveshaft on rear wheel drive vehicles.
Most likely a dirty fuel filter or Bad Ignition Timing.
A simple solution may be to run a higher octane gas. Another quick potential fix is to change the spark plugs. If either of those don't work, it's most likely a timing problem.