
Finlanderboy |

Escape (Su): Each time the inquisitor using this judgment hits an opponent with a melee or ranged attack, she can use a move action attempt to create a diversion to hide (see the Stealth skill).
I honestly do not know how this works in able to use it.
I am not sure what a bluff distraction would be needed and the dcs or checks. Also the action economy.

Archaeik |
You can use Bluff to allow you to use Stealth. A successful Bluff check can give you the momentary diversion you need to attempt a Stealth check while people are aware of you.
If your observers are momentarily distracted (such as by a Bluff check), you can attempt to use Stealth. While the others turn their attention from you, you can attempt a Stealth check if you can get to an unobserved place of some kind. This check, however, is made at a –10 penalty because you have to move fast.
The way I read it, if you make a successful attack, you may spend a move action to move, making a Bluff check (opposed by Sense Motive), which if successful, allows you to make Stealth check(at -10) if you can end your move in a square that offers cover/concealment. (Abilities that modify stealth like HiPS notwithstanding.)
I think the benefit of this judgement is that normally, the action economy would be Standard:Bluff->Move:Stealth, so this allows you to get the attack in addition.

Quandary |

The phrase 'can use a move action attempt to create a diversion to hide' seems like it is missing a reference to a Bluff check, i.e. that as a move action you make a Bluff check to Create a Diversion to Hide.
I don't think the Move Action includes movement, all it does is a distraction.
So if you Standard Action "Attack", Move Action "Escape" (Bluff Check), you only have a 5' step left normally.
It's not spelled out, but I believe the Diversion automatically means that they can't see what square you move to while you are moving there,
so if you can Stealth there they don't know where you are, if you can't Stealth there (or fail) they DO later notice where you are.
Since there is nothing restricting it to the same turn, you could also activate it after you hit an enemy with an AoO, which leaves you much more movement/action options on your turn. Really, the wording there is vague, since there is just no time limit given, every attack vs an enemy for all eternity could entitle you to use this Move Action "Escape" (Bluff/Distraction) at any time you choose.