I have exactly the same problem. A post somewhere on the Intertubes suggested manually adding "client charset = UTF-8" to the odbc.ini file, which I did without success.
Has anyone successfully gotten ODBC data out of FileMaker 11 in Unicode format?
UPDATE: almost as soon as I posted this, I found the answer. Using the Actual Technologies ODBC Manager, in the "Database Information" pane, you click the "Advanced Language" button. In the resulting dialog, uncheck "Auto-detect language settings," then check "Application uses the wide ODBC API," and finally chose "UTF-8" in the Multi-byte text encoding popup. After this, it works correctly.