Laning phase:
Aatrox's lvl 1 to 3 is weak so you going to have to wait till lvl 4 to start fighting with your laner but before that you going to have to play very safe because you Q has a very long cool down so you can use your Q only to take minions or for poke and you can loose some minnions if your laner is aggressive. After lvl 4 you get very strong you start looking for fights with your laner and you can even do a 1v2 againt enemy laner and jungle but you need to land your full combo and also it depends on the champians as well
Mid Game:
Your mid game is very strong here you start looking for team fights and try to get objectives with your team, don't try and split push he does not do damage to towers, but you can split push to bring enemy team to fight you to secure objectives and don't forget that you can use your ult not just for fighting but also for escaping.
Late Game:
In the late game after lvl 16 you start to fell off because you can't put points on your Qs anymore you will be weak compared to the othrs.
How to play him with the items you have:
Try to build Black Cleaver as first Item sine it gives very good stats like damage health and a lot of Ability hast then you get Iceborn Gauntlet as a second Item, this item will make sure you land every Q after AA-ing the enemy because of its passive which put a big slow on the enemy. For the rest of the Items it just depend on the game and every game is defferent so you items might change but Black Cleaver and Iceborn Gauntlet second is a your two first items in every game.