Something like this should work for you:

#!/usr/bin/perl

use warnings;
use strict;

my @to_match = qw/his her theirs/;

START:
for my $line (<DATA>) {
    for my $item (@to_match) {
        next START unless $line =~ /$item/;
    }
    print $line;
}

__DATA__
his her theirs asdf
his her something else
this shouldn't match either
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