You want to strip the wires as to expose the least possible wire necessary to get into the connectors. Make sure the connectors are wide open to accept as much cable as easily as possible. Tinning the wire, as suggested above, will provide the cleanest installation. The suggestion of pin connectors is great, but doesn't work at all in a one gang box unfortunately.
I have definitely taken a large gauge wire and taken off a few of the strands before to make things work. It's not ideal, but works just fine as volume controls themselves are going to bring down the audio quality, you aren't going to lose much by pulling out a few strands of the speaker wire and creating a more solid and reliable audio connection to your volume control.