Is it normal for the green oil light to come on when the door is open? I noticed that when I push in the door buzzer switch it turns off again. I never noticed this before.

Yes, it doubles as the door open lite.

No, it's not normal.

But it's an electrical problem, not an engine problem.

any ideas on where to start?

Electrical gremlins are the worst, get the colour diagram off of this site and an ohm-meter and have fun.

Does your oil light also come on when the oil pressure is low?
If not, I bet the problem is under the dash, pull out the gauges and trace the oil light wire. Awkward, but easy. You'll probably find those clear square plastic faston terminal junction thingees that allow you to join four wires and it's the door switch junction that someone wired into by mistake. Then look for the lost and lonely faston terminal from your oil pressure sender.
I hope its that easy!

Dave