Here's a page with a description of the standard plug.
The tip of the plug is the left channel, the ring is right, and the sleeve is ground.
All you need now is a multimeter to determine which colours correspond to those contacts.
Looking at pics of your headphones I see they're the kind where the wire goes to one side, and then the other side's wire goes through the neckband. If the soldered red white in the pic go to to the other side through the neckband, my guess would be that you should just solder the red and white from the plug to the same contacts, and the blue to the contact without any wire on it.
That's just my guess.