Why do you call that "old-style"? Zip cord is still recommended and used, although perhaps a heavier gauge. Don't you want to use them? Much better than "wireless" speakers, which aren't wireless (they need power).

Some of those wires look like lamp cord that was used in a DIY job.

And nobody bothered to push the wires in during painting.

Problem is, to safely bare the wire ends for voltage measurements, all the circuit breakers would have to be turned off prior to separating the wires and taking insulation off.

If you're concerned that one of these wires might be "hot", then get a non-contact tester which will tell you if any of the wires in the box are hot.

Is it likely that, if these are for a home theater or music system, the small boxes are for speakers and the large one is for the AV receiver? How many wires are in each box? Do you want to reuse this?

Whatever the wires are, that work was done by a amateur. You could have zip cord carrying house current in the walls, which is a huge violation of the electrical code. Or you could just zip cord for carrying low voltage audio signals which weren't labeled and were confusingly put in the same kinds of boxes that are required for normal house wiring. Given how many wires there are, I'm a little suspicious that they would simply be for a set of speakers. If you aren't electrically savvy and know how to use a voltage tester, have a knowledgeable friend or electrician check this out to see if the wires can be traced and if it's a hazardous situation.