Oil pressure gauge sender is at the back of the engine (typical) next to the distributor. Probably single prong connector, brown wire. Pull that off, with key in "run", touch that to ground, and see if gauge moves. If it does, sender problem, if not, wire or gauge issue. That should be your first test, although if the needle is "stuck" at something other than 0, turning the key to run should also "zero" the gauge.
The voltage that the voltmeter "reads" is typically what also provides power to other gauges or lights, so that might be tied into the oil pressure issue. You'll need to pull the gauge cluster to check this though, you will need to verify the + on the printed circuit board is getting 12V with the key in "run".