What are the chances that my fiance will get to stay if his visa has already expired? How?

More information is needed in order to fully analyze your fiance's immigration options, but generally if you are a U.S. citizen, your fiance entered the U.S. lawfully and with inspection, and you and your fiance become married, the two of you may pursue adjustment of status through an application in the Immediate Relative visa category. This would be true regardless of whether your then-spouse may have overstayed a visa. It would be wise to consult with an immigration attorney who, after learning all of the relevant information, could advise about immigration eligibilities, options and strategies and offer legal representation for the application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.