if i got frigid tough on a spell storing armor
and it goes off at the first strike of an enemy full attacking me i would then hit him with it he becomes staggered.
would his full attack stop because he is now staggered and can only do 1 attack or a move action??
Yes.
Well, there's the peculiarity of spell storing armour not actually doing anything because you can't take a swift action outside your own turn, but assuming the ability is meant to work as an immediate action rather than a swift, yes. There's an FAQ on becoming staggered in the middle of your turn.
spell storing is available for armor so I am guesing that the armor can only go off if you saved your swift action that turn.
or would it be a thin what you can only use when hit by an aoo?
One of the devs has mentioned that the spell storing armor property is supposed to be an immediate action.
Yeah, it really should be an immediate action. It is on our list of things to fix.
This, combined with the FAQ on action limiting conditions acquired mid-action:
Yes, even if it interrupts or limits your in-progress.For example, if you are making a full attack and attempt to trip your opponent, but you provoke an AOO because you don't have Improved Trip, and your opponent has a spell storing weapon that's storing a hold person, and you fail your save against the spell, you are immediately paralyzed and can't take any of your remaining actions (including the remainder of your full attack).
Likewise, if your opponent had the Staggering Critical feat instead of a spell storing weapon and the attack staggered you, you would immediately gain the staggered condition, which would prevent you from taking any actions that violate the staggered condition's limitations. If you provoked by taking a move action to move through the opponent's threatened area, you could finish that move action but could not also take a standard action after it. If you provoked as part of a full attack (as with the trip example), becoming staggered would end your full attack at that point and prevent you from taking a move action after the staggering attack. It doesn't matter if the AOO happened because of your first attack in your full attack or your last allowed one, being staggered ends your full attack at that point because you can't make a full attack if you're staggered.
So, Frigid Touch is stored in your armor. Enemy makes a full-round attack action, hitting you on his first swing. You choose to let loose your stored spell, and the attacker is hit with frigid touch, taking 4d6 damage and becoming staggered for 1 round. Since he is now staggered, and can not technically take a full-round action, the FAQ ruling comes in play and basically says that any inability to perform the action you are performing stops the now illegal action. So no more attacks.
It is a shame, in this situation, that spell storing armor automatically hits it's target with its touch spells, so you don't get to roll for the chance at a critical, which makes frigid touch SO much more powerful (staggered for 1 minute is HUGE against a BBEG).