I have seen quite a bit of debate about whether or not Strong Jaw and Improved Natural Attack stack with each other. Do they or don't they, and why?
Officially, Improved Natural Attack and strong jaw can't combine for a cumulative effect
Size increases and effective size increases: How does damage work if I have various effects that change my actual size, my effective size, and my damage dice?
As per the rules on size changes, size changes do not stack, so if you have multiple size changing effects (for instance an effect that increases your size by one step and another that increases your size by two steps), only the largest applies. The same is true of effective size increases (which includes “deal damage as if they were one size category larger than they actually are,” “your damage die type increases by one step,” and similar language). They don’t stack with each other, just take the biggest one. However, you can have one of each and they do work together (for example, enlarge person increasing your actual size to Large and a bashing shield increasing your shield’s effective size by two steps, for a total of 2d6 damage).
(Emphases and links in the exchange's reply mine.) The feat Improved Natural Attack increases the damage of one of a creature's natural attacks "as if the creature’s size had increased by one category." The spell strong jaw says, "Each natural attack that creature makes deals damage as if the creature were two sizes larger than it actually is." (Emphasis in both effects' quotations mine.)
As both the feat and the spell are effective size increases that use language nearly identical to that used in the FAQ, their effects don't stack.
Threads arguing about the interaction between these two effects may have been created before March 2015 when this exchange was added to the FAQ.