So you have Calibrum, Severum, Crescendum, Infernum, and Gravitum.
Calibrum is basically a giant ass snipe.
Severum is useful for if you've been chunked out in a fight and want your HP back as you heal 200 / 300 / 400 HP (this healing doesn't stack with the amount of champs you hit), but because Aphelios will also automatically AA every single target hit by his ult so it will also apply Severum's healing effect on top of that.
Crescendum is the one for the most damage in a 1v1 situation because of how much DPS the chakrams provide. It produces three additional chakrams on top of those from the champs you hit (you can get up to 8 if you hit 5 champs).
Infernum is great for supplementary teamfight damage if the enemies are all stacked up on top of each other (think 5 man Amumu ult into Infernum Moonlight Vigil). Aphelios can win fights by himself with a well placed Infernum ult.
Gravitum is great for engaging or starting a teamfight as you get the AoE 99% slow into Gravitum's root if you keep it as your main weapon. If you have a team that can follow up on your CC it's bonkers.