What ODBC driver are you using. Depending on the manufacturer and version it may not support any of the Large Object Binary (LOB) datatypes. For example, see the following link for a discussion of Microsoft's ODBC agent for oracle limitations.
You hit the nail right on the head. It wasn't Access's fault, I was using an older ODBC driver. While I don't have access currently to which version actually worked, if someone later has the same problem and wants to bump this thread, I can find out (the DSN that worked was set up by someone who left for vacation on Monday).