It's doable, but there's no real elegant solution. Take a look at Acme::use::strict::with::pride, which turns on strict everywhere. (Actually it turns it on at the top of each file - there's nothing to stop the file including no strict later on.) It does this by installing a coderef into @INC which rewrites modules when they get loaded.

Personally, I'd take a different approach. I'd cheat by taking advantage of the fact that nearly all code everywhere uses strict, and hook onto strict's import function. Save the following code as Taint/Obnoxious.pm:

package Taint::Obnoxious;
use strict;
use re ();
my $orig_import = strict->can('import');
*strict::import = sub {
  re->import('taint');
  goto $orig_import;
};
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Now, running your program with perl -MTaint::Obnoxious should do the trick. All code that uses strict will also automatically use obnoxious tainting.