Greg,
Your best bet is what Russ said. Twist the stripped wires to longer heavier wires, at least 22 gage, solder them together to get a good connection, then insulate them with anything from tape, shrink tubing, acorn nuts or one of many types of crimp connectors. The problem with some crimp connectors is that they are somewhat bulky, and acorn connectors can come loose and fall off. Just what ever you use, be sure you have a good connection (flux and solder the joint first), then be sure it is insulated from shorting out to other wires.
There was a discussion about using "liquid tape", and that seems to have worked for some that have used it.
I hope this is the information you are after. If not, let us know.
Don