There really isn't a direct route. You will need to make at least one transfer.
If you take the train, my understanding is that the entire train is loaded onto the ferry from Messina to the mainland. It might be the simplest way, but it is a very long trip. You would still be required to go all the way to Naples and then change to a different train or bus to Sorrento - OR train to Salerno and bus to Sorrento.
Look into a flight from Catania to Naples and then short bus-ride from Naples airport to train station and then train to Sorrento. It requires a flight, bus ride and train, but it's fairly straightforward, likely won't cost much more and will save you significant travel time.