What are the permissions on /usr/local/lib/perl5/site_perl/5.6.0/aix/auto/DBD/Oracle/Oracle.so, in particular is it readable by whatever user the webserver is running as? (Which is likely to be "nobody".)

I have not seen your problem but the first error reported is that that file cannot be loaded, and the second is that permission was denied. I would ignore the guess made at the higher-level DynaLoader code...