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Wheels are out of balance
lose bolt no seriously its probly your alinement is off
You may have a bent wheel, defective tire where a steel belt has shifted or broken, worn steering parts, and possibly a defective wheel bearing.
shifted or broken belt in the tires
Engine miss.
You have a warped rotor. Brake pads need replacing and the rotors turned or replaced.
This question can be referring to two separate conditions. If the steering shaking while the brake pedal is being applied the condition maybe warped rotors. If there is steering wheel play while the vehicle is stopped and or moving it is an indicator or worn or failed column components.
Tires out of balance, bent wheel, worn suspension or steering parts, bent driveshaft.
If the steering wheel is loose while driving the steering rack may be going bad. A bad steering rack leads to a lot of play on the actual wheel.
Probably warped brake rotors. They can be removed and resurfaced or replaced with new ones.
I'm assuming that your steering wheel has locked. Try jerking the steering wheel back and forth while turning the key to start it.
Steering columns commonly lock when the ignition key is removed. If the key doesn't want to turn and unlock the column, shake the steering wheel side to side to try and release it from the binding lock while turning the key.