It sounds like you are asking about flying on one ticket from Catania to Rome, then another ticket from Rome to Oakland, all on the same day.
If this is the case, how lucky do you feel? If there's any problem, you will be responsible, both logistically and financially, for getting a new ticket from Rome to Oakland - at last minute prices.
In a similar situation, I flew from Catania to Rome a day early, then had dinner in Rome, so that I wouldn't have to worry about missing the flight home. You may feel more comfortable with risk than I am.
Different airlines from Catania to Rome arrive at different terminals in Rome; Norwegian departures use Terminal 3. Even if you arrive at T3, I'm not sure if you can stay behind security when transferring. If you are checking bags, you definitely can't; you will have to pick up your checked bags in Rome and re-check them to Oakland before going to your next gate (Norwegian will not interline bags from other carriers).
If you do want to fly in to Rome the night before, note that there are numerous flights a day from Catania to Rome on multiple carriers, so you can choose a late one. Looking quickly on Skyscanner for the randomly chosen date of October 11, 2017, I see flights leaving Catania at 8:30 and 9:55 PM.