GGO, the GA Supreme Court found a right to privacy in the GA constitution that prohibits the state from enforcing its sodomy law against consenting adults (in private and not on the town square). I didn't look for cases regarding adultery and fornication laws, but the same logic would apply to them as well.
Fornication and adultery are both misdemeanors (OCGA 16-6-18 and 19, respectively).
Note, however, that even though adultery probably is no longer punishable as a crime, the state still "punishes" adulterers in the form of divorce. Most states that still have substantive "grounds" for divorce include adultery as one of the grounds.