Your car needs an alignment. Typically around $100 or less.
A worn out power steering pump, or steering box.
You probably need to get your tires balanced. Or replaced. If the bias goes (steel belt breaks or shifts), the car will waddle at low speeds, and the steering wheel will shake at high speeds.
The steering wheel wobbles, because of the unconditional pressures from the ground that is adjusted at speeds when it reflects gravity.
Check your power steering fliud, if it is low this could cause the vibration you are feeling.
Clunking/knocking sound felt though steering wheel and floor when turning and going over bumps at low speeds.
Could be out of balance Tire may be worn and need replacement Could be a bent wheel
go get 2 new tires and have the alignment checked on it
1996 c60 truck if you turn steering quickly at low speeds vehicle shacks acts like drive train until you stop
the rear wheels turn with the front at high speeds, and opposite at low speeds.
Loose or worn out power steering drive belt. Usually this is a loose or worn belt on the power steering pump. The pump works its hardest when the vehicle is parked or at low speeds so if there is a belt issue, it will happen then.
Means your steering wheel pump might be going bad. But first check your steering wheel fluid you could be very low.