What sounds wrong to me is that you want to do a ODBC connection between OBIEE and an Oracle DB, why not connecting with the OCI driver?
Is the connection pool configured correctly with the right "call interface" and parameters?
Did you install the Oracle database client on your Linux machine to get the OCI drivers? Alternatively, you could just use JDBC instead which is already shipped with BI.
Also, make sure the datasource name in your reports match the JNDI entries you create in OBIEE.
You can't use JDBC connections from the RPD.
The 'ODBC' error is a BI Server error, and it's because the BI Server can't find the tns you've set up. tnsping will validate it with tnsnames in the current path, but BI Server may be looking elsewhere - check the docs for where to put it. Alternatively, use EasyConnect syntax in the RPD.