If your car has significant mileage it is likely that the rubber grommets of the rear suspension arms are worn out. If so the rear end is no longer aligned and the rear will virtually steer the car and behave precisely as you describe. The steering wheel will be off center because the front wheels have to compensate for the rear misbehaving.
1993 190E 2.3
2000 Toyota 4x4 Tundra