Does the client-based Oracle ODBC driver support SQLDescribeParam?

In versions of the Easysoft Oracle ODBC driver before 2.1, no.

Oracle doesn't support describing parameters, so the Oracle ODBC driver does not fully support the SQLDescribeParam ODBC API. This prevents you from using some applications and interfaces. Since 2.1, we've added the DESCRIBE_PARAM_AS_STRINGS odbc.ini setting (Linux and UNIX) and the Describe Parameters data source setting (Windows). This setting adds the SQLDescribeParam ODBC API, which describes all parameters as strings.