This will cause a small voltage to be present at the receptacle. With the switch off i suspect the phantom voltage is being picked up by the adjacent live wires.
File Inductor Switch On Off Positive Voltage Png Wikimedia
Why do i have voltage when switch is off. A basic neon test light is good for verifying no power. When the switch is off the only way it would be zero is if the switch shorted the inputs together. You should not be able to get voltage here. Put a 1 meg resistor across the input on the meter to kill stray readings then measure the voltage. A wiggy does not have phantom voltage issues it is great for troubleshooting open circuits. I would think it will read 0 volts.
Not enough to activate the load just enough for the light in the switch to work. This is perfectly normal and very basic. With the breaker off i suspect the phantom voltage will be less. If the wire is not energized but the terminal of the circuit breaker is energized while the breaker is switched off then the circuit breaker is faulty and would require replacing. If the wire is energized when not attached to the circuit breaker then there was two power sources providing power to one circuit. If they are both off we can turn the plug on with either one but if one is in the on position the other switch does nothing i know this is a common wiring goof in three way switches but we.
When the switch is off one of those two wires should be connected to nothing at all. I doubt it does unless you wired it that way. Its possible the switch is defective and it allows a high resistance connection even when off. In the off position the light passes a small amount of current through itself to the load.