I can't be of any specific help but your odyssey definitely smacks of a wiring issue, the biggest possibility that comes immediately to mind is one of the wiring harnesses has contacted a ground source it was meant to be isolated from.
I would painstakingly inspect every inch of every wiring harness looking for an area that's typically already close to metal and/or a hot surface. One of my friends with a 2003 Chevy van recently had an issue with his transmission not allowing the van to start---it turned out to be a single wire inside a harness leading back to the PCM had contacted an exhaust pipe. Once it was temporarily moved away all was back to normal.
These things are frustrating and test the patience of mechanics and diagnosticians. I don't know that there are any diagnostic computers capable of detecting an errant voltage due a short circuit.
In the end I'm sure this will be a quick and relatively cheap repair---the key being finding or identifying it first.
Be persistent and hang in there---hoping for a good outcome!