Help! What in the heck is going on here?

[dreidel13]

I am trying to power an outside light (never worked). When I flip the breaker, power comes out at both the black and white wires. When I undo the wire nut and separate the black wires the power changes. I am not sure if this us a 3 way setup of not. I haven't found a switch that would complete that setup. I thought I could remedy this easily, but the way the power comes out I'm not sure I can do that safely. There is small amount of power coming from the neutral and ground when the breaker is on. I dont want to tear the wall apart. There is no attic for me to drop a new wire. Thoughts? Help?

 

[Marvo]

Don't trust that tester, those non-contact type testers are very prone to being oversensitive and giving false readings. Rather use a proper voltmeter that will display an accurate voltage.

 

[dreidel13]

Don't trust that tester, those non-contact type testers are very prone to being oversensitive and giving false readings. Rather use a proper voltmeter that will display an accurate voltage.

Yah, I know they are sensitive. It's just an easy way to show where there is current. Mostly I'm concerned about power coming out of both wires where the light is supposed to hook up and also current in the ground wire.
Any suggestions as to what is going on?