Would be a big shock if he chose the Celtics. Has the chance to play with an up and coming team in the Cavs or with Lebron James in South Beach. Those are the two places he went to school/grew up as well IIRC.
In the end he's going to go to the Heat. He's a better fit in Boston or Cleveland, but South Beach, Lebron, and the destination 95% of all players want to play at for the chance of a dynasty.
I would be surprised, but not shocked if he went for BOS. Cavs have by far the most to spend if he's looking for short-term $, but I don't see them as an up-and-comer by any means being one of the worst teams in the NBA. Lots of cap, lots of picks, lots of rebuilding for an extended period of time. Cavs lack the exposure Oden would get elsewhere, and if they struggle as seems likely, it depresses his market value compared to the Cs and Heat (unless Oden really shines). Don't know that much about him, but if he's a Midwestern guy at heart, then BOS and MIA are at a disadvantage on that level.
Miami has South Beach, a crown, and likely another ring in its future (but bet the house against winning 7 crowns). Heat, however, has no cap room on the horizon unless they blow it up (a possibility because they are going to get whacked hard by the new CBA). If Oden puts in 2 years there and plays decently, he could parlay that into a better contract down the road somewhere other than MIA.
Boston has lesser charms than MIA, but its cap situation is much better than MIA's. Cs have cap after next season and he'll get more exposure for the market than with the Cavs. Boston does have some advantages. Doc Rivers would have to be rated the best of the three coaches, the Cs' heritiage, and mentoring potential.
That all being said, bet on the best short-term money: Cavs.