But, for some reason the installation on my company provided desktop or even on the unix server does not have this module (or it was stripped from base installation for some reason).

DBI & DBD::Oracle are not part of the core perl distribution, so they would have been installed by somebody at the other places you've worked.

How do I connect to oracle databases without DBI module??

Well, I guess you could drive one of the command line tools - but I wouldn't recommend it.

I cannot install or build it on my machine , coz I do not have enough rights.

Talking to your sysadmins and getting them to install it, or getting the rights to install it yourself will almost certainly be simpler than attempting to roll your own solution.