I'd rather not open and close the file more than once: disk accesses take time (there's the cache, you didn't mention your file's size). Instead, I would first generate subs that count a given character and store them in a hash, referenced by that character.

Then, for each line in the file, loop over the letters and call the sub from the hash. Increment a counter which is itself stored in a hash.

#!/usr/local/bin/perl
use strict;

my @letter = qw/ a b c x y z /;

my %subs;
my %counts;
foreach ( @letter ) {
  $subs{$_} = eval "sub { \$_[0] =~ tr/$_// }";
}

while ( <DATA> ) {
  foreach my $letter ( @letter ) {
    $counts{$letter} += $subs{$letter}->($_);
  }
}

print "$_: $counts{$_}\n" foreach @letter;

__DATA__
aedj dfas jijiojsdf dsfwfy jiox jiohjdfax jojojdjj, oiiia oioje asfdc 
+oujsdfayx soujfosdxjpoiojfdxjljojaois jojojx jopjpx jojoijx joijiodfx

asdfasdf jjalsdf jlajkldf jojiojsd jiojasj ioj wwdn jojae jojocjoc joi
+jss jiojwx jiojoxuiojy joiyu oiuouyy
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--bwana147