PA applies to melee damage rolls. Bulette rampage is a damage roll in melee. Breaker rush is not a damage roll and it would not apply to that.
Adding the same ability mod to the same thing twice without any kind of type is a no-no. "When he performs either combat maneuver, he deals an amount of bludgeoning damage equal to his Strength bonus", and "whenever you succeed at an overrun combat maneuver check against a foe, that foe takes an amount of damage equal to 1d8 ... + 1-1/2 times your Strength bonus." is trying to add the same ability mod triggered by the same action and doesn't look like it'd work.
Another question. Does "add Dex Mod to AC(untyped)" and "to AC(Dodge)" count as same source?
No they're different, but all dodge bonuses stack with each other anyway as a deviation from the general rules on stacking from same source.
Cause in the Overrun case, Breaker Rush makes blunt damage and Bulette rampage makes untyped.
This is a good question, but I kinda think of this as taking 2 levels of paladin and swashbuckler for Charmed Life + Divine Health = 2x Cha to saves. So I'd say negative ghostrider.
I don't have any rules lawyer BS to add, but if it smells like cheese...
I can see the bludgeoning vs untyped argument... but it still smells like cheese.
Cheese perhaps, but since one of the instances of strength being added has a type (missed that) and the other doesn't you can add both.