As a free action, this might be a reasonable feat. As a standard action, it can be advantageous but only in very limited circumstances.
1. Only against undead--this is a very big limitation; comparing this to Divine Might, for instance, Divine Might makes turning ability useful against any enemy.
2. Only when dealing damage is more effective than turning. This is also a big limitation since turning will often be more effective than damage against undead. So, it is useful only against unturnable undead or by characters who aren't very good at turning anyway--perhaps a multiclassed cleric or paladin. This also underscores the opportunity cost of using the feat: a use of it could have been a turning attempt and since you're obviously facing undead, a turning attempt might well be useful. Contrast this with Divine Might which doesn't have much of an effective opportunity cost most of the time since it can be used against creatures against whom turning is useless.
3. Only when the standard action you lose is likely to inflict less than (2d6)xthe number of attacks in the rest of that round and the next round that are likely to hit. So, for an unhasted 3rd level paladin with a 15 strength wielding a +1 longsword (1d8+3--average 7.5), Divine Vengeance is a bad idea. He gets an average of 7 damage in round 2 but gives up an average of 7.5 damage in round 1 (where it's potentially more useful).
In a best case scenario, Divine Vengeance could be quite useful--for instance, a hasted Ranger/Rogue/Paladin/Consecrated Harrier 10 with all of the dual wielding feats going after a vampire who is the target of his hunt (Blessings of Scripture +10

In that case, he might end up exchanging 25-30 points of damage from the hast action for an additional 30d6 (7 attacks/full attack action plus one from haste in the second round) points of damage from Divine Vengeance. (On the other hand, most level 16+ paladins--even multiclassed ones have more than a +7 cha bonus so he could get even more damage by using Divine Might--a feat that is easier for him to get)
This would be a much better feat if it were either:
A. A free action to activate.
B. Also effective against evil outsiders or any creature with the [evil] subtype
or
C. Lasted 2 rounds+1/point of charisma bonus
It could probably be beefed up in all of these ways without being overpowered.