Edit: Seemed I needed to "enter strategus as a hero" first... though I don't know what the hell that did, frankly, haha.
There are two ways to participate in strategus:
1) As a hero: means you appear on the Calradian map, where you're able to move, trade, collect army etc, it's not connected with your cRPG character in any way (except your hero has the same name ofc).
2) Fighting as mercenary for either side in strategus battles: you apply, and if you get accepted you have to join NA3 (or EU3, depending on what part of map the battle is) in time, where you use your
Main characted with it's build but with equipment of your side.