I think you are asking what penalties/bonuses apply to an AoO in rounds following Power Attacks, and can you choose to power attack on an AoO if you didn't do so during your previous turn. You are also asking if you can smite on an AoO.
Power Attack
On your action, before making attack rolls for a round, you may choose to subtract a number from all melee attack rolls and add the same number to all melee damage rolls. This number may not exceed your base attack bonus. The penalty on attacks and bonus on damage apply until your next turn.
You may only choose to power attack, or not, on your turn. Once that decision is made, it applies until the start of your next turn, including all AoO's that occur in that time frame. Thus, you cannot choose to Power Attack on an AoO; that decision was determined during your previous turn, and applied there as well.
Smites are a little less clear. In core, we have three examples of Smite abilities: the Destruction domain, the Paladin's Smite Evil, and the smite ability of (half) fiendish and celestial creatures.
Once per day, a paladin may attempt to smite evil with one normal melee attack.
A paladin can smite with a "normal" melee attack. So your ability to Smite Evil on an AoO is dependent upon your DM's interpretation of "normal." It doesn't say it has to be during your turn. Is an AoO a normal attack? To use the language of 4th ed, it is a "basic" attack, which would be "normal" in my book. But your DM may not agree.
Destruction Domain
Granted Power
You gain the smite power, the supernatural ability to make a single melee attack with a +4 bonus on attack rolls and a bonus on damage rolls equal to your cleric level (if you hit). You must declare the smite before making the attack.
All that is required here is that you make a melee attack, and you declare the smite before you attack. This one is good-to-go on AoO's.
Smite Good (Su)
Once per day the [fiendish] creature can make a normal melee attack to deal extra damage equal to its HD total (maximum of +20) against a good foe.
There's that word "normal" again.
Keep in mind that if you are performing a full attack, you might get 4 attacks, and you can smite using one of them. That info might sway your DM to allow you to smite on an AoO.
