That's homebrew, allright. Odyssey, no. Not even close. While the pics make it look kind of hack, there are some interesting design elements. The rack and pinion is a good thing, just not sure how stable it is with the angled shaft and u-joints out there in space like that.
The rear suspension is funkadelic! Coilovers aren't too surprising, but the radius arms are! One thing I do NOT like bout that rearend is the fact that the brake rotor is on the jackshaft. If you lose your secondary chain, you lose your brakes. Not the safest design.
Get rid of the seat- too bulky and heavy.
With the size, potential weight, and obvious intended use, I would suggest a big-block engine (11+ HP) and a CVT like the Comet 40. Anything less would offer disappointing performance.
EDIT- Took me a minute to figure out what was bothering me about that axle- got it! Since I can't tell by the pics, I need you to have a close look. Are there any more linkages to that axle other than the long radius arms? Here's the issue- That axle may move up and down as a unit, equally on both sides, and that's just fine. BUT- if the two sides can move up and down at a different rate (articulate), that's going to throw the chain faster than you can say, "it threw the chain again".
Look for a central "hinge" that will allow the axle to go up and down, but constrain all other movement.