Convert the dates to a numerical, fixed-width, greatest significance first format. For instance, if you have Feb 12, 06, you could translate that to 060112, then compare numerically:

use strict;
use warnings;

my $date1 = dateconvert('Jan 11, 04');
my $date2 = dateconvert('Jan 30, 04');
my $date3 = dateconvert('Feb 10, 04');

print "$date1 <= $date2 <= $date3 ? ";
print $date1 <= $date2 && $date2 <= $date3 ? "Yes" : "No";

BEGIN {
    my @mon = qw/Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec/;
    my %mon; $mon{$mon[$_]} = $_ for 0..$#mon;
    sub dateconvert {
        my $date = $_[0];
        my ($mon, $day, $year) = $date =~ m/(\w+) (\d+), (\d+)/;
        $mon = $mon{$mon};
        return sprintf("%02d%02d%02d", $year, $mon, $day);
    }
}
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This is easily modified for different formats by changing a couple lines in the function.