I'm at war with the Greeks and they destroyed all of Rome and my allies. I'm down to my main settlement and their army is closing in. What should I do? They offered a protectorate treaty but I denied because I don't know what it is.
Nothing you can do. At least not in this circumstance.
If you're unable to defend that last settlement, it's game over. That's why it's important to, even if you know you're losing, to take as many enemies with you as possible, so that eventually they won't have enough forces to finish you off.
Ideally you should not even lose a large part of your demesne, but sometimes things happen, and that's fine!
Regarding the protoclast thing, it's a common theme on Total War games. It essentially means that you're going to work for them. You retain your remaining holdings, but you will start paying them a part of your revenue each turn. On the other hand, you become allies, which in turn prevents you from being put on a game-over situation, for now.
A Protectorate Treaty means they will stop attacking you, usually for a price (an annual tribute to be their friends). The AI is so fickle they might turn around and decide to attack you the very next turn though, so it usually isn't worth it.
Breaking a Siege
Because of the simplicity of the AI, you can easily lure a sieging army to its death (assuming you have undamaged stone walls, archers, and cavalry).
Once an enemy lays siege to your settlement, attack them and place archers on the walls nearest their troops, and cavalry near the gate. Depending on your archers, they may or may not be able to hit the enemy troops from the wall, but the enemy might move them a little farther back.
Send out a cavalry unit to lure troops close to the wall, letting your archers thin their ranks, keep doing this until your archers run out of arrows. You may suffer a few loses to your cavalry unit.
After you run out of arrows, increase the battle speed and wait. Eventually the enemy will grow bored and sound retreat from the battlefield.
Slow the battle speed back down, and charge and destroy the retreating troops with your cavalry. Since they are in retreat, they won't turn and fight back, and it is easy to run them down from behind, giving your troops maximum advantage.
This was the easiest way I found to break a siege with minimal loss of forces. Since you can do this with 2-3 archery units and 2-3 cavalry units (and maybe your general) against 2000 units, you will often receive a Heroic Victory at the end. This should allow your general to earn Good Siege Defender and possibly Warlord (since you don't appear to be playing as a Roman faction).
This should allow you to destroy any invading armies while allowing you to build up a sizable force to take back some of your territory.