How many staff are needed to support aviation on an aircraft carrier?
The ship's complement for a Nimitz class carrier is 3200. That is the crew required to maintain ship operations.

A further 2480 crew comprise the Air Wing - everyone needed to perform duties directly associated with flying activities, including maintenance, ordnance handling, emergencies, etc. It's treated as a separate entity because any one of ten Air Wings could be embarked on a carrier at any given time.

That is a total crew of 5680.

I couldn't find a breakdown of specific trades or ranks for either entity.

Source: Wikipedia

Note that the newer Gerald R. Ford class carriers make extensive use of automation, and so have several hundred fewer crew members in the ship's complement.