The first three quests are not necessary to complete. You can start with and take it from there. Once these quests have been completed Weaken the Ramparts becomes available from Stone Guard Stok'ton.
Once inside the group must slay each of the Fel Orc leaders. The following contain tips and strategies for defeating each:
Quick, there isn't much time. Thrallmar's existence balances on the razor's edge!
We're caught between Hellfire Citadel in the west and the Burning Legion to the east. With the Legion's attention turned toward the Dark Portal we must take this opportunity to strike at the fel orcs of Hellfire Citadel. The key to this is to first break through their ramparts!
Go there, slay their leaders, and then bring back proof to Caza'rez across the room from me!
<name>, right? Stok'ton told me to be expecting your report.
I trust that you bring good news?
It's a good start. With those three dead their forces should be in disarray. And with their artillery up there silenced we'll have an easier time getting close enough to take the citadel!
But there's more to this than meets the eye - I can feel it - so I'm going to have something else for you to do.
For the time being, though, you've done well. Take your pick of any of these from the Thrallmar armory.