Strange wiring in outdoor flood light. How to explain why previous “electrician” did it this way?

So the floodlight in the back of my house doesn’t work, I also have a handful of mystery switches so I figured I would open up the fixture and make sure it was wired right (or at all, I’ve found a handful of switches and fixtures that just weren’t connected). Anyway, I opened it up to look at the wiring and I found something very strange. How can I understand what is going on here?

Here’s a photo of the wires:

And here is a drawing of the circuit:

Obviously because I can’t draw white lines with white I did that with yellow lines. Also as you’ll see from the schematic, three power lines come into the electrical box. And apparently (checking with my multimeter) there is actually power coming through on the white wire, not black. Very strange. Also those two unterminated white lines didn’t even have wire nuts on them, it was just insulted wire. So I stripped them and covered them with wire nuts (not in the photo) to make sure there was no possibility of any arcing.

I’ve checked the voltage going through the white and black lines that connected to the light were only carrying about 5V of power so I figure that’s got to be phantom voltage. When I connect the hot (white) wire with other wires I get about 60V, not 120.

How can I explain what is supposed to be going on here? I’ll probably have to call an actual electrician to look at this but what are some potential troubleshooting that I can do to fix it and/or figure out what is supposed to be done correctly?