Outlet box has voltage when a device is plugged in on another circuit
This very much sounds like a case of what is called Open Neutral.  This can be a very serious condition, depending on where it is.  Where you plug something in that results in a voltage somewhere else, do plugged in equipment or lights operate properly?

An Open Neutral is when the neutral wire of a circuit is disconnected or not making proper contact.  The result is the one or more receptacles are in series with a different group of on or more receptacles and 240 volts is being applied.  If the loads are unequal, one load will get a higher voltage (more than 120 volts) than the other.  Where more than one load is in a group, shutting of or unplugging one thing can raise the voltage on others in that same group.

This condition requires a licensed electrician to resolve.  The only action you should consider, in the mean time, is shutting off the main breaker or main disconnect or pulling the main fuse block.