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.