So if I were to make a Staff Magus, Magic Warrior, Hex Crafter (all Magus archetypes), would I treat each archetype as a separate class in which to invest level or do they act as though they were all one class simply trading out abilities for the ones each archetype modifies or removes.
You can take as many archetypes as you want as long as they don't have an effect on the same ability. All levels you take (in this case, to Magus) apply to the class and all its archetypes.
A character can take more than one archetype and garner additional alternate class features, but none of the alternate class features can replace or alter the same class feature from the base class as another alternate class feature. For example, a fighter could not be both an armor master and a brawler, since both archetypes replace the weapon training 1 class feature with something different.
As a note which was reminded me in comments. You cannot multiclass to same class to gain other archetypes.