I just killed everyone in this camp except for one person that I can't kill.
When he is about to die he falls on the ground and gets up afterwards, then starts attacking me again.

Hes name is: Legate Hrollod

So, what do I do to take over this camp? I'm a Stormcloak

Bump. -.-

You can't kill him If you are Imperial you also can't kill the bosses of the Stormcloaks

While you are able to remove the Imperial encampments, you technically cannot. Each Imperial camp has a NPC that is labeled essential. No matter what you try they will not die. There are several NPCs in the game that are labeled this and cannot be killed.

So like in Oblivion.

Damn it. I hate the immortal NPC stuff.

So do most of us. It would be much more interesting to get notes by courier saying one of your camps was under attack or being able to take over other camps for various bonuses.

Yeah, this made no sense to me either. The game actually tells you to go attack the camps, but it won't let you clear it.