I have been running into a lot of that funny wire lately. It looks just like any other wire I have used for years - but it won't wet right. Upon closer inspection, I see some of it was copper coated steel wire ( magnet attracts it ). Some of it was copper plated aluminum ( wonder how they did that ), and other was plain old stranded aluminum wire ( it was a dollar-store USB cable I bought to hack into for a source of five volts ).
It looked great until I tried to solder it. At first it would seem to wet, then solder just rolled off it. Not even GOOT flux worked. What happened is the solder dissolved the thin layer of copper off. Must have been electroplated on. When I took it to the lab and saw what was going on under the microscope, it became obvious what the problem was.
I guess with today's technology where most everything is crimped, aluminum and steel wire is a lot cheaper than copper wire and works good enough to avoid a customer return.
Google sent me here while I was seeing if this situation existed. The evidence left here shows that is indeed what is going on. I leave my experience for others also trying to figure out they were losing their mind because they can't do something they have done for years.
You should use a wire stripper or a pair of pliers to strip insulation from wire. Small wires can be stripped with your bare hands: just pinch the insulation with a fingernail and yank it off. If you catch it just right, the insulation tears and slides off, but the conductor is left intact.
It sounds like by burning the insulation, you have fouled the metal with the products of combustion of the plastic. This layer will prevent the solder from flowing onto the metal and bonding with it. Even if the plastic was completely vaporized, it's likely that the metal oxidized. Solder does not like oxidized surfaces. To solder, you need clean surfaces free of oxidation or other residue. (Other than soldering flux. Speaking of which, you should have some and use it!)
One of the functions of soldering flux is that, being mildly acidic, when it gets hot, it etches away the thin layer of oxidation from copper. It will probably not eat through the carbonated remains of burnt insulation, however. Still, it is worth a try. If flux doesn't cut through, then just cut a piece off the end of the wire and try again, and this time strip it mechanically rather than, err, pyrognostically. :)
Update: if the wire insulation is just a fine lacquer (similar to what is used on wire used for winding voice coils or transformers), it may be possible to solder with the lacquer in place, with better results than torching the lacquer. Some hobbyists spray lacquer on DIY circuit boards, without covering the solder pads, and solder right through it anyway.
It may also be possible to remove the lacquer by using a solvent such as acetone.
Best Answer
I would NOT use a knife or sharp edged tool of any kind on thin wire. Very fine sandpaper if you can strip a large area and then clip the end of the wire to just the length of stripped wire that you need to solder.
If you can only strip a very short area for soldering, then I would burn the insulation off with a soldering iron, and tin the stripped end and examine it before actually soldering the connection.
Using a knife can cause nicks in the wire, which will later break when things vibrate.
I used to use this trick when soldering wire-wrap wire. I always burned the insulation off the wire, one of my coworkers preffered to use a wire stripper. When we got stuff back that wasn't working, it was always the ones my coworker did - the wires broke off where he had stripped them.
You'll need to get a blob of solder on the tip of your iron, then poke the wire in to the blob so that the point of the wire touches the surface of the soldering iron tip. The point of the wire to the soldering iron tip helps to heat the wire itself and melt the insulation from the inside. The blob of solder helps to heat the insulation from the outside. It takes practice to be able to do this quickly and accurately, but at least you won't have to worry about the wire breaking later.