You need to have at least 1 opposing faction to start a multi-player game against AI, as well.
By 'your territory' do you mean the countries are the same colour on the map, or the countries are highlighted by the player's colour on the map, so they specifically control that area? If you start off with an elvish country, you still have to move troops to the neutral elvish countries in order to take them over.
If two opposing factions move to the same neutral country, or one faction moves to a country already occupied by another, there should be a battle.