What is the easiest way to "detect" electrical installations (wires in wall)
Studfinders usually have AC detection circuitry, but they only work if there's power in the wire.
These are $20 or so, and you run them along the wall to find the wires.

To detect which socket/circuit they are on, have an assistant turn off the breakers one by one until the studfinder stops flashing, and then go back and use a test light to determine which socket it is connected to.