If you have another free socket nearby, set the meter to measure AC volts, and touch one end on earth in socket, other end on whatever you're testing. Note it is normal for there to be a small number just from the leads even if not touching anything. You're looking for anything "bigger". I'm not sure what threshold to set as concerning, but certainly 50v+ is.
I still have a suspicion that if there is some fault in either the power cable of PSU that might potentially also give the symptoms you're seeing. Even if you can't replace the PSU without getting another one, do you have a spare power cord you can try swapping?