If you are working with a 64-bit OS, you will encounter a problem which was not typically faced in the days of 32-bit OSes--namely, that you will have a separate set of 64-bit ODBC Drivers vs. a set of 32-bit ODBC Drivers.
So, when you type odbcad32.exe at the Run Command, you are ACTUALLY opening up the 64-bit ODBC Drivers that have been installed on the machine and NOT the 32-bit ODBC Drivers.
The 32-bit drivers can actually be found by typing the following path at the Run Command: \windows\SysWOW64\odbcad32.exe. Therefore, if you are looking for the 32-bit Oracle drivers, you will only find these ODBC Drivers available in the 32-bit ODBC Drivers area.
When you open the ODBC Dialogs as well, you should look closely at the Title of the Dialog as well:
When you open the default ODBC Dialog, you will see a title of "ODBC Data Source Administrator (64-bit)".
However, when you open the 32-bit ODBC Dialog, you will see the following title instead: "ODBC Data Source Administrator (32-bit)"
If the titles match up, then you know you are in the correct place!!