In addition to that, the Oracle driver cannot find the texts for its error message, which is, of course, not good, but could also be caused by missing environment variables.

Can you connect with sqlplus? If you can, the Oracle client software should be working.

This is say because when redirect the shebang line to another perl installation path with same modules installed it works fine.

You have multiple Perl installations on the same machine? Maybe DBD::Oracle is confused about which Perl to use. Try to run some simple test scripts from the command line (just connecting) against both Perl versions.