TNSNames.ora doesn't appear when setting up a oracle odbc driver connection
You probably use Win64.
If yes then you must configure ODBC DSN in the same Windows subsystem as Oracle. Check if you installed Oracle client in 32 or 64 bit version.
There are 2 version of odbcad32.exe in 64 bit versions of Windows. In c:\windows\system32 you will find 64 bit that configure ODBC for 64 bit applications and will use setting from 64 bit version of Oracle client. In c:\windows\syswow64 there is 32 bit version you should use to configure ODBC for 32 bit programs including 32 bit version of Oracle client.