towing with a Honda Oddessy

I would not tow any hybrid with any minivan.

Max hitch weight will be the actual weight of the vehicle when fully loaded for travel, passengers and cargo complete, subtracted from gvwr from the dot safety plate on the vans door post. Remember weight of tongue is always much more than the brochure number which is empty weight, since they can't possibly know how you will load the trailer or how much weight you will load. Good luck / skip

Ascend makes some small lightweight fiberglass sided ones. as does R-pod.
bumpy

Any idea what the hitch weight the van can handle is?

Check out some of the smaller CampLite trailers, don't bother looking at the ones that have a dry weight of over 3000 lbs.

CampLite

You could probably also get away with some of the fiberglass trailers, up to the 19'er might work.

Escape Trailers

when I was looking at the Pilot, at that time it was rated to tow a 3,500 lb. TT and a 5,000 lb. boat. don't know about the oddessy however.
bumpy

only a handful of hybrids will have GVWRs of 3500lbs. and they are around a max of 17'. but nearly all have very low CCC numbers.
some will only have 100-200lbs. for cargo, battery, propane and water.

but your problem is that the frontal area of a hybrid, will exceed the frontal area limits on any minivan, except the Astro/Safari minivans which are no longer made.
any conventional hybrid or travel trailer's frontal area will exceed your van's max amount.
second issue is the van's payload amount. when you add passengers, cargo, WDH and tongue weight, it'll probably exceed the van's payload amount.