1. Make sure you have installed the Oracle 32 bit driver
2. Make sure you create your DSN in the 32 bit registry. To do this you use ODBCAD32.exe found in the wow64 folder (not the standard windows system32 folder, which is where the normal ODBC Admin shortcut on the start menu points to)
As already mentioned, MS Access is a 32 bit application. It only talks to 32 bit drivers, and only looks in the 32 bit registry for DSN's.
The 32 bit Oracle client should talk fine to the 64 bit Oracle installation, as it is communicating over TCP/IP (not in-process)