According to the PRD:
Offensive Defense** (Ex): When a rogue with this talent hits a creature with a melee attack that deals sneak attack damage, the rogue gains a +1 dodge bonus to AC for each sneak attack die rolled for 1 round.
Note that rogue talents marked with a double asterisk (**) in this list add effects to a rogue's sneak attack. Only one of these talents can be applied to an individual attack, and the decision must be made before the attack roll is made.
Now, Dodge bonuses stack with themselves, so let's say I had a Two-Weapon Fighting Rogue with a Sneak Attack of +5d6 who managed to hit a flanked foe twice in the same round (10d6 sneak attack total), does that mean that the Rogue gained a +10 Dodge bonus to his AC or a +5 Dodge bonus?
Also, as it reads, the Dodge bonus applies to all attacks that target the Rogue's AC, not only the those from the creature who took the sneak attack damage, correct?
This is discussed in the faq for APG. It doesn't really reach a conclusion, but I would start with reading it and discussing with your GM.
Nope. This was either FAQ'd or rewritten or something. I can't exactly remember what the change was, but it was clarified that it would not stack.
If for no other reason, there is this generic FAQ that is about stacking in general:
Do ability modifiers from the same ability stack? For instance, can you add the same ability bonus on the same roll twice using two different effects that each add that same ability modifier?
No. An ability bonus, such as "Strength bonus", is considered to be the same source for the purpose of bonuses from the same source not stacking. However, you can still add, for instance “a deflection bonus equal to your Charisma modifier” and your Charisma modifier. For this purpose, however, the paladin's untyped "bonus equal to her Charisma bonus (if any) on all saving throws" from divine grace is considered to be the same as "Charisma bonus (if any)", and the same would be true for any other untyped "bonus equal to her [ability score] bonus" constructions.
So what happens is the same source of something can never stack. Hitting with Offensive Defense twice and having it stack would be stacking the same thing twice (or more).
So, Offensive Defense does stack with other dodge bonuses from different sources, but not with itself.