So the tracks were recorded elsewhere? If you did the recording, describe the entire chain(sometimes, folks new to recording make mistakes such as connecting an external preamp to the Mbox XLR input, or as crazy as renting an expensive mic, but singing into the wrong side of it
yes, I've seen that too).
Sadly, once they are overdriven(maybe at the mic, or at the preamp), there's not a lot that can be done(but if someone has an idea, I'm keen to learn)
Maybe you can turn this around by using the distortion and going for a unique sound like some of ZZTop's stuff, or Foghat, where the vocals are distorted?
If the music just doesn't lend itself to that kind of "sound", your best bet may be to re-track vocals.