We towed a popup with a Pilot, which is the same engine and trans as an odyssey, but I think it does have a stiffer suspension.
It did do pretty good with it, but it did lighten the front end some. Our Pilot was all wheel drive, and when starting going uphill in the rain, you could feel the front tires start to spin, and then the rear drive would kick in, so not sure how much spinning the odyssey would do.
It does not have wiring for a brake controller, but you can wire one in. I did that on our Pilot, it is not to bad, but you have to run wires the length of the car underneath it, so that is a bit of a pain.
Etrailer.com had a kit for it with all the wiring you need, and even had a video on how to install it.
