Do Competence Bonuses Stack Pathfinder?

A competence bonus (or penalty) affects a character's performance of a particular task, as in the case of the bardic ability to inspire competence. Multiple competence bonuses don't stack; only the highest bonus applies.

Do enhancement bonuses stack Pathfinder?

No. No enhancement bonuses stack. No bonuses of the same type stack, except for dodge and circumstance bonuses (but good luck getting those to raise your Strength).

Do untyped bonuses stack Pathfinder?

Rule 1: Untyped bonuses also stack. Different stats that effect the same thing will stack by consequence. For example +2 enhancement bonus to str and +1 enhancement bonus to a weapon with give a total of +2 to hit when using str for an attack.