I have been towing a 2619 for a while, we went up to the sequois. It had no problem making it up the hills, If I recall I was in 2nd or 3rd gear all the way up traveling at about 35 miles per hr. If you do it be sure you have the tran cooler installed. Mine is a 2007 odyssey we had myself my wife and 2 kids.
I just purchased a 2011 Pilot 4wd. I can say there is a difference in towing I don't feel the trailer as much now. But I can not beat the mileage in the odyssey it was between 16 and 17 mpg.
Either way I don't think you should have any problems with the odyssey. Just don't overload it