If the key switch is off and the lights are on, and you disconnect the connector at the ignition switch and the lights go off then it would appear that the switch may be bad.
With the switch being off the entire car should be off. If the power goes out to the lights when disconnected then you may be getting a feed back inside the switch that may energize other circuits when not commanded to be on.
This is a weird problem and you need to check all components with a volt/ohm meter before changing any parts.
I'm not saying this is the problem but it may be part of it.
What would cause the feedback inside the switch though? Does it matter that its just the radio that is powering on? I know you said lights but wasn't sure. The stupid steering wheel acts like a power switch for the radio sometimes even if I wobble the wheel back and forth on lock with keys out, the radio will, from time to time, toggle on and off.
Also, what voltages should I look for and at what components? I'm sorry I'm so full of questions, this thing is killing me though. My friend who usually does my electrical work on the car had suggested the switch that's why I'm trying to narrow it down there. The darn switch is $112 though. :-0
Also which side of switch do I unplug? The one into the harness on car or one from the key cylinder?
I would take the steering column apart to see what is going on inside the column. For you to wiggle the wheel and the radio goes on and off I would suspect the switch.
I was really afraid you would tell me to take it apart. Great. So if nothing is wrong in the column I am probably buying a switch huh? I'll keep it updated. Guess I'll go see what it takes to get into the column.