I have 2 unidentified wires in the wall, also black and white, the plug is working
How do I tell if any are ground wires?

Hot to ground will immediately trip breaker or blow fuse. The black and white could be hot and neutral or part of a switch loop for a switched outlet. Do you have a VOM or a neon tester and can you test for voltage? Any black tape or black marking on the white?

Probably be better to use a no contact voltage sensor. If the black and white are hot and neutral a volt meter will show voltage. If the black and white wires are a switch loop, meter will not show voltage. Volt sensor will show voltage regardless.