Simply look to the Catholic states of the past, especially the Middle Ages, as a guide for how these crimes should be punished.

Abortion, sodomy, obstinate formal heresy, and blasphemy are capital crimes deserving of death.

Adultery, fornication, prostitution, lewd public dress, etc. are still serious crimes, though not capital ones. These would be punished by imprisonment, public flogging, fines, etc.

Skipping Mass on sunday without valid excuse is already punishable with the pain of Mortal Sin, I'm not sure if the State ever imposed any corporal punishments for trsngressions like that. At least, I can't readily think of any that did (I'm hardly an expert so take that for what it's worth).

Also it should be noted that while it is the duty of the State to punish these crimes as they are a grave harm to the common good of the public, it has also been the practice of Catholic states to respect the sancrosanctity of the family as an autonomous entity to itself; the mantra "a man's home is his castle" was taken quite seriously, and you would therefore not see the State intervening in matters of the home, like enforcing proper catechesis of children, or checking up on Mass attendance for the members of the household, forcing Baptism on babies etc. Catholic states were sensible of perennial Catholic teaching that the family is the nucleus of society, and that the father as head of the family has a certain autonomy that arises from the Natural Law itself and so avoided meddling in matters of the home as much as possible.