Here's a regex-based approach. (I agree, however, that a parsing approach may be more appropriate.) It doesn't handle single-quoted strings, but should be easily extensible to cover such. I'm not sure it gives you exactly what you want, but I think it comes close. The critical (IMHO) regexes require Perl version 5.10+.

use warnings;
use strict;


use Test::More
  # tests => ?? + 1  # Test::NoWarnings adds 1 test
    'no_plan'
    ;
use Test::NoWarnings;


use constant TEST1 => <<'EOT';
# this is a comment, should be matched.
# "I am not a string" . 'because I am inside a comment'
my $string = " #I am not a \comment, because I am \" quoted";
my $another_string = "I am a multiline string with # on
                       each \t line #, have fun!";
EOT
# print qq{[[${ \TEST1 }]] \n\n};  # FOR DEBUG


use constant C1 => '# this is a comment, should be matched.';
use constant C2 => q{# "I am not a string" . 'because I am inside a co
+mment'};
use constant S1 => q{" #I am not a \comment, because I am \" quoted"};
use constant S2 => q{"I am a multiline string with # on
                       each \t line #, have fun!"};


# these regexes compatible with 5.8 (and prior? 5.0?)
my $comment = qr{ [#] [^\n]* $ }xms;
my $string  = qr{ " [^"\\]* (?: \\. [^"\\]*)* " }xms;
my $comment_or_string = qr{ $comment | $string }xms;


# these regexes require 5.10+
my $comment_only = qr{ $comment | $string  (*SKIP) (*FAIL) }xms;
my $string_only  = qr{ $string  | $comment (*SKIP) (*FAIL) }xms;


VECTOR:
for my $ar_vector (
    [ TEST1, $comment_or_string, C1, C2, S1, S2, ],
    [ TEST1, $comment_only,      C1, C2,         ],
    [ TEST1, $string_only,       S1, S2,         ],
    ) {

    if (not ref $ar_vector) {  # must be a note...
        note $ar_vector;
        next VECTOR;
        }

    my ($text, $rx, @expected) = @$ar_vector;

    is_deeply [ $text =~ m{ $rx }xmsg ], \@expected,
      # qq{},
        ;

    }  # end for VECTOR
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