This is one of the rare cases where I would recommend slurping the entire file rather than reading line-by-line. I feel that the simplification justifies the use of much more memory.

#!/usr/bin/perl
use warnings;
use strict;
use Slurp;
use Data::Dumper;

my $strings = join '|', qw( AB AC AD AE FG );
my $counts;
for my $file (glob ('File/*')) {
    $counts->{$_}++ foreach (Slurp($file) =~ m/($strings)/gms);
}
print Dumper($counts);
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