Jayco has several models within your towing range. The ROOs tend to be heavier for a given length, but the 17 likely is in range.
Some other brands also have models that can be pulled by your Odyssey.
Please keep in mind that the trailer will be heavier than the Dry weight before you load it, and heavier again after you load it. You'll likely want to stick with something in the 2600-3000 lb range. (Towards the lower end of that you plan to take more stuff.) Plan on towing with empty water tanks, and filling at your destination. You can also save weight by carrying little food and buying that at your destination too.
You'll want a good weight distribution hitch.
Tow at 60 mph - plan the time and distance of your trip accordingly. (The tires on the trailer will almost certainly be rated for a max speed of 65 anyway, and the cheap tires used are not known for being over-engineered.)
I've found my Sienna to be a pleasant TV - been towing this trailer for 6 years.
