All the trannys are from Japan on the Ody, and I think this holds true for all Hondas sold in N. America. I have never seen one with a transmission country of origin anywhere else but Japan.
My understanding from reading an article in Car and Driver is that the 5sp is fundamentally the same unit as the 4sp, but with a gearing change that allowed them to get 5 forward speeds without much internal changes. The ratios are different for 1-4, as is the final drive ratio. Whether or not the 5sp develop problems remains to be seen. It's my understanding that the vast majority of the original units never develop problems, but those that do typically suffer the same symptoms. Service manager told me that there was an undersized bearing in the early units, and since that was fixed all has been fairly good. If failure occurs during factory warranty, a Honda rebuilt unit is installed. If outside factory warranty, whether customer has HondaCare or not, a rebuilt unit from "Howard Engineering" is installed. I was told that the Howard units are performing as well as teh Honda rebuilds. Hope that's true. Was also told the Honda rebuilts essentially have all new internals but a used case. The use of a used case prevents them from being able to call them "new." All this from dealer service manager. He's never steered me wrong yet.