If I have a character that has either incap or mindcontrol or tk and superstrength and I have the meteor object held in a close combat attack can I choose to use the object?

my first reaction as being a former judge was no, however...

it never states that the character can not use the object, it just states that they do not have to use the object...

the reason that this still applies to no damage attacks is that it is not expressed that the no damage is a replacement effect (however it is highly inferred as otherwise it would most likey be governed by the rule of 3)

as such this same problem crops up with Releasing a captive....

and even if the no damage ones fall through it certainly makes incap interesting...

No damage attacks deal no damage. You can't modify no damage.

For example, a critical hit using Mind Control does not deal an extra point of damage (or do anything other than automatically hit, really).

does a critical miss still deal damage to the attacker? if mind control is the focus of the attack?

Nope. A no damage attack has no damage.

that may be so but you guy are still not addressing incap which is a zero damage not a no damage attack and critical hits on incap do add to damage

as such the op has still not been completely answered

Sure. He can choose to use the object. It won't do anything, though.

With Incap, the damage becomes 0 for the action.

so the can not be modified further from the meteor will not prevent the incap from modifying damage to 0

No. Incap doesn't modify anything; it replaces the damage value, making the damage value become zero.

Meteorite does not have any effect on replacement values.