The usual way is to grab a AA battery and connect the two ends of the wires to it. If you hear a pop in a speaker, then those two wires belong to those speakers.
Then, to see which is + and -, you connect the AA again, and see what way the cone of the speaker moves. If it moves outwards, the wire that is connected to the + of the AA battery is the +.
Stock speakers will survive, but dunno how good it'll sound
If you're getting new speakers, i'd recommend re-doing the wiring. It aint that hard