I cut the wire on my headphones. If I press the clean cut together
trying to adjust their position, I can get sound. If I strip the
wires and connect them individually I get nothing at all. Can anyone
help me understand this?


I got caught on this one too. It wasn't headphones but a int/ext temp gauge.
The external line broke and I stripped the wires and resoldered them. No
output.
On closer inspection, the two wires were actually very small shielded
wires (I'm not too good in the eyesight department these days) and I'd
stripped the outer and the inner insulation in one go.
Have a closer look at your headphone wire.
Alan