His voice he uses sound rather similar to an infamous portrayal of another evil emperor whose name also starts with C. Phoenix quite clearly seems to be imitating that actor with his performance. After all they both play evil emperors who murder their predecessors, and they both wish rather for a relationship with their sister which is far too close. Phoenix really imitates this earlier performance, and really I should not even say imitates but rather really rips off the earlier performance. He has the same evil voice, self-indulgent manner of movements.
Phoenix I suppose is creepy but any actor could be creepy quite easily since the character himself is simply just that. He really does nothing more with his character than one would expect. Phoenix sort of attempts to bring more to Commodus but it is mostly fairly random. Some of the time he makes him a man desperate for support of some kind, but this is often thrown off by a weird gesture just to be a strange villain. Phoenix is an actor with a unique presence so this is not a complete failure of a performance, but a better performance could easily have come out of this character even with this actor.