That's a pretty light tow vehicle. Honda says that its tow rating is 3500 pounds, and the inevitable asterisk goes on to say that to reach that rating, the vehicle must be equipped with the optional factory-installed "surge-type or electric trailer brakes, load-distribution hitch and transmission- and power steering-fluid coolers." That tow rating also assumes that the vehicle itself contains only the driver and no cargo. If you add passengers or cargo, you must subtract their weight from the tow rating. And of course you must add a Class 3 (2-inch) hitch receiver, electric brake controller, a 7-pin electrical socket at the rear bumper, and wiring.
The 3023 was one of the heavier TrailManors. I believe the spec for "dry weight" was just above 3000 pounds, dry weight being the weight before any factory installed options (air conditioner, awning, etc) are added, and without any of the stuff you will want to put in the trailer - food, clothes, dishes, tools, maybe water and propane, and so forth. It is common for the weight of a loaded-and-ready-to-camp TM to run close to 4000 pounds.
Having said all that, we have a number of Forum members who have used an Odyssey as a tow vehicle. If you search the Towing and Hitching forum (where you are reading this) for the term "Odyssey" in the title, you will find a number of posts.
Good luck.
Bill
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