I built a turbo Civic back in the early 2000's, cost about $4K and I ran Hondata 3BD (like an S300 today). Still have the car, but I pulled the turbo on it and shelved it. Wasn't gonna pass emissions like that since I ran an open downpipe.
I also bought a turbo Civic, built D16Y8 and dyno tuned to 270 hp at the wheels. Ridiculous to drive. So much fun!! Then emissions laws changed and now IT can't pass emissions because of the ECU being tuned so it has no OBD2 communication. Still have this car as well, not sure what I'll do with it.
I will also likely be turbocharging my 93 Saturn wagon at some point. plan is to use the turbo out of the Civic and a megasquirt ECU for tuning. That car only gets a tailpipe test, so I should have no issue passing.
But I doubt I would turbo the Odyssey. If I was to build a fast van on the cheap, I'd get a Montana and swap in a supercharged Grand Prix or Regal engine in there... or GXP or whatever they call them. Easy plug and play, all bolt in, emissions legal, loads of performance parts. Can prob get about 400 hp from a mostly stock block bolt-in swap. Little air to water intercooling, little overdriving pulley, little tuning... have a fast Montana. Also lowered suspension options from the W-body cars and Pontiac Torrent rims, have a bomb little van for prob less than $4K all in. Maybe even less!