Odin was originally called Win32-OS2. It was originally designed to translate Win32 binary types and catch application calls to the Win32 libraries and implement that functionality in OS/2's 32-bit APIs. It was, in a way, rather like the Micrographix Mirrors library which came with OS/2 2.0 to let application writers "easily" produce apps for Win16 and OS/2. Mirrors and Win-OS2 (which ran Win3.x apps) made it easier for OS/2 users to run Windows apps, but helped kill native OS/2 development ("We don't need to produce a native OS/2 version because the Win16 version runs fine.").
Odin isn't complete. I don't know if it's missing functionality which would let it host Opera/Win32.
Mozilla/2 is looking pretty good (or was when I looked at it last). Opera's going to have trouble finding an OS/2 market, IMO.
Cheers,
Scott.