As far as making the body of the trailer strong enough for off-road travel there are a couple of options. One option is to make the body out of a steel skeleton. I did this on my first trailer and I think that it would be pretty sturdy off road. This trailer is approx 5' wide by 5' tall and 10' long in the body. Incidently this one is for sale also.
The other option that I have used is to dado the floor and bulkheads into the side walls. This will in effect make a torsion box and you gain a lot of rigidity in the body from this. Here are a few pictures of the dadoed walls of two different trailers.
If you want the wood trailer body to be stronger still after you have glued and screwed the dadoed walls together with the floor and bulkhead you can always add an epoxy fillet to where they are joined. This is a technique that would be borrowed from wood boat construction.
Hope that this gives everyone some more ideas on what is possible.