At room temperature? Methylene chloride?
At high temperature, soldering heat does it, for "Sold-Ez" types.
Ask the manufacturer, it varies by formulation. Some high temperature enamels (polyimide based) have to be removed mechanically, or chemically with some very unsavory substances.
If nothing else, if you find you need fire -- fire leaves scale (copper oxides). These can be removed with a strong flux (usually acid), but acids cause corrosion later. I find it's better -- and much more exciting (wear PPE) -- to use a spoonful of molten NaOH. This melts around the melting point of lead, and forms salts of everything involved (lead and tin oxides dissolve, forming the respective {plumb|stann}{ite|ate}, while copper oxide becomes the strongly blue sodium cuprate; metal particles floating around tend to turn the melt gray or black, though). Quench the wire in water and soak until the lye and salts are completely dissolved. Do not get NaOH in your eyes if you want to keep them; melt can spatter, quenching NaOH releases fumes; etc. All the usual stuff.
Acetone.
Yikes! Your wire has terrible enamel, for your own sake dispose of it and buy new!
Tim