At least this does not fail any of the test cases you have provided :)

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11140211
use warnings;

my $data =<< "END";
head1|head2|head3
val1|val2|val3
val1|val4|val5
val6|val4|val5
val2|val7|val5
val3|val7|val3
END

open my $fh , "<", \$data or die "can't open input file $!";
my @headers = split /[|\n]/, <$fh>;
my %seen;
while( <$fh> )
  {
  my @row = split /[|\n]/;
  $seen{$_}{shift @row}++ for @headers;
  }
print join "\n", "UNIQUE VALUES for $_:", (sort keys %{ $seen{$_} }), 
+"\n"
  for @headers;
[download]

Outputs:

UNIQUE VALUES for head1:
val1
val2
val3
val6

UNIQUE VALUES for head2:
val2
val4
val7

UNIQUE VALUES for head3:
val3
val5
[download]