Does anyone know the best way to clean a hard rubber mouthpiece ? I understand that if they are treated wrongly they can turn a green color and smell of sulpur dioxide, like wrotten eggs.

fill a sink w/ luke warm water, add two squirts of dial soap or something like that and take some q-tips and scrub the inside/outside of the mouthpiece. Don't hold it underwater too long, just dip it in for a few seconds, take it out, and scrub and repeat it for a few minutes

I use a method to clean and sterilize the mpcs.

a vial of vinegar
I place the mpc in it (cork up and not in the vinegar) for 10-30 minutes then use a brush (old toothbrush is a good alternative) to clean out any gunk.
I may repeat if necessary

then clean in water
then I may dip in mouthwash to sterilize (then sometimes water again)