You should do all of these by train, and I wouldn't personally trust Rome2rio as a resource.
Trenitalia is Italy's national rail service, and you will need to use their trains for almost all of your journeys.
https://www.trenitalia.com/en.html
Venice to Monterosso will be a long haul.
If you are staying on the island of Venice, you will be departing from Venezia S. Lucia station
You will arrive at Monterosso station.
It will take 5.5 hours to 7+ hours, and involve at least 2 trains changes depending on which trains you choose.
Monterosso to Siena will take at least 3.5 hours and involve at least 2 train changes.
Siena to Sorrento will be another really long haul: at least 5 hours and at least one train change to Napoli Centrale, and either local Circumvesuviana commuter train or ferry (you would have to transfer to the port) to Sorrento. Add at least another 90 minutes. You could also purchase a private driver from Naples if budget allows (at least 100 euro).
Sorrento to Rome will be either ferry to Naples, transfer to Napoli Centrale and fast train to Roma Termini, or cheap (but not very comfortable) Circumvesuviana commuter train or private driver to Napoli Centrale and then fast train to Termini from there.
A critical piece of info we need? Are you going to Rome at the end of your trip to stay there for a few days? If you are only going there to fly home form Fiumicino, you don't want to be in Sorrento the night before your trip; spend the night before the flight in Rome. Termini is Rome's central train station and not Fiumicino's.
A great resource for boning up on Italian trains:
https://www.seat61.com/train-travel-in-italy.htm