What could be causing strange voltage readings?
Are the wires color coded? (they should be). Black is the "Hot" and White is neutral. If you had a three wire system the bare wire or a green whire would be the safety ground.

Next I would recommend that that there is a much better and safer way to debug your wiring. First turn off all power to your house by shutting off the main breaker. Since you do not know exactly where your wires go, that is the only way to guarantee that they are not hot.

Now use a wire tracing kit like this one from Triplett or something similar.
 That way there will only be low voltages on the wires and you will not risk electrocution or a fire.