Earphone/headphone wires are a PITA because they're so tiny. I'm impressed you managed to separate them and strip the insulation down as well as you did. Normally I just toss them and buy new ones because it's not worth the hassle.
But if you really want to fix it, as described above twist the matching colors together. Get a soldering iron and melt a tiny bit of solder into the twist in each wire to hold it together. (I'd suggest heating the solder directly, instead of the wires like you normally do - with wires this small you could melt the insulation.) Then wrap each individual wire with electrical tape so it doesn't contact the other wires. Then you can wrap the entire 4-wire bundle with electrical tape, overwrapping both...