If you want to use the continuity setting of your meter to test, do this:
Testing the wiring - Engine off, disconnect the wire from the switch. Test continuity between the end of the wire and the engine case. If there is continuity, then the wire is shorting to ground somewhere.
Testing the switch - Engine running, test continuity from the terminal on the switch to the engine case. If there is continuity, then the switch is bad or the oil pump is not producing enough pressure to open the switch.
Don't blame me if your motor explodes while running, though!
I'd test the wiring, and if that checks out OK, then replace the switch. If the light still comes on, then your problems are more significant.