Wow!! A tough debate. Hard to know which side to come in on.
First off,
Hi Caliban.
Long time no talk with. How are you doing?
Ok, back to rules.
With regard to "wield", I do think that you wield the weapon up to and including the point in time where you actually do damage (or miss). The reasons for that are:
a) you get your strength bonus if you hit, even after the weapon has left your hand
b) you get the enhancement bonuses of the weapon if you hit, even after it has left your hand.
If it is not being wielded (i.e. used) by you, then it would not get YOUR strength bonus. If the item was not being "use activated" at the time of the hit, then it would not get the enhancement bonus for damage.
In addition, I think it is clear from the general wording of Weapon Special Abilities and the wording of Spell Store specifically, that you not only get your enhancement bonus of the weapon, but you also get to use all special abilities of a weapon when you use it (just like a thrown flaming dagger) and in this case, you can also have the weapon cast the spell (similar to a dancing weapon which is not in your hand, but you get to use its special abilities).
The word in that description that allows it is the word "immediately". Yes, it is a free action, but it is an immediate free action explicitly called out by the definition of the special ability. The special ability does not state that any time the user wields the weapon or any time the weapon is in the users hand, etc. Rather it states:
"Any time the weapon strikes a creature and the creature takes damage from it, the weapon can immediately cast the spell on that creature as a free action if the wielder desires."
This is not very debatable. Regardless of whether OTHER items like Chaos weapons give this ability or not to the wielder, THIS item does. The capabilities of the Chaos special ability is non-sequitor to any discussion of the capabilities of the Store Spell special ability. Just like the capabilities of the Store Spell special ability is non-sequitor to any discussion of the capabilities of the Chaos special ability.
Now, having said all of that, it is also quite clear that Vampiric Touch in this item does not give the hit points to the wielder of the weapon. He is not casting the spell. The weapon is. The special ability description is quite clear on that. In fact, the weapon gets the temporary hit points which makes the weapon more difficult to destroy (since weapons have both hardness and hit points). Granted, whether the weapon gets temporary hit points is debatable since the temporary hit point section of the PHB explicitly discuss characters and does not discuss inanimate objects. But to me, hit points are hit points.
Now, people can feel free to argue it, but I would suggest that you cite rules if you want to sway anyone. The rules I am citing are those that are explicitly known (i.e. wielders strength applies after the weapon leaves his hand, hence, he is wielding it at least until it either misses or does damage and the spell store item can be used by the wielder but the weapon itself casts the spell).