I solved this problem of "Can't locate strict.pm: Permission denied"... today 2018-01-28. The reason was: because some directories have been created by the "cpan" command when I tried to use it under supervisor account root.

So, remove theses directories (backup them before!):

sudo rm -rf /usr/local/lib/perl

sudo rm -rf /etc/perl/CPAN

rm -rf /root/.cpan/

That's all! and perl programs will run again without error.