Your radio definitely shouldn't be drawing that much juice unless you've got some serious system in there. I'm guessing this is an aftermarket radio? I really don't have any leads on what could happen to cause this though, the radio shouldn't be hooked to the trucks wiring system except to get the voltage, maybe power antenna, and ground.
If the oil pressure gauge is moving, unless engine RPM's are actually dropping too, that tells me that somewhere a wire is messed up that somehow ties the radio and volt/oil gauges together, or the radio *is* drawing that much, (again you'd have to have some serious stereo going for that to happen) and the alternator isn't able to handle the load.
My 78amp alternator doesn't fluctuate at all when I turn the stock radio on.