I think the play is weak and very difficult to be successful at. The main weakness in doing an oak bluff is that it is usually out of character for a strong player. It smells of tells, and anyone with a hand is going to call you, unless they are a weak passive paranoid player.
I kind of think any semblance of success with this bluff is not that one made a successful bluff, it is that the other opponents actually missed a draw of some kind.
However you asked so here is my best opinion.
•against what kind of opponents
Tight risk aversive opponents. You can spot this type by following Dan's guidelines. They are experienced player but not very good. They are the kind that is always whining about missing a hand. You can tell they have missed a hand easily and you should bet into them whenever it looks like they missed a flop, or river.
•against what kind of range we put the villain on
The opponent will have second pair or worse with a draw to a flush or straight. How your opponent sees you is more important, even very tight players will look up a loose cannon with second pair.
•on what kind of boards
Hard to say. Any board could qualify, that depends more on the players in the game and your specific opponent.
•on what kind of history (if any) with the villain
The opponent will be very tight, and proud of his great laydowns, may have shown some. Like DH says make sure it is someone that has laid down hands to small bets.
An oak bluff will not work against many players, it should really be something that is simply the obvious thing to do when you do it.