Loose or worn tie rod ends on the 96 F350 can cause this problem. There could be other front end components wearing as well, check the entire front end system for problems.
A steering wheel oscillation is an indication of a bad tire or bent rim.
To roll when driving typically refers to moving the vehicle with minimal acceleration or coasting at a slow speed without pressing the gas pedal. It can be done when approaching a stop sign or traffic light to conserve fuel or maintain a steady pace.
If you are referring to the steering wheel wobbling whilst driving along, then you probably have one or both of the front wheels out of balance. If the wheel wobbles at a certain speed then it may be a problem with the front locking wheel hubs or a bearing problem.
You have probably bent a rim and knocked the vehicle out of alignment. Don't drive it too far until you've had a chance to make the necessary repairs, otherwise you'll destroy the tire. It may also have some control problems which may result in unsafe driving conditions.
Steering fluid leak.
A car's steering wheel will vibrate when driving if the car's alignment needs to be adjusted.
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.
A steering wheel that is padded with leather for comforment when driving
No. Steering is just one element of driving, but there are a lot more, such as controlling the speed and being vigilant as you drive.
wheel bearings
probably going to lose your steering
you may need more power steering fluid.