If you really want a fixed number of entries then this variation of NewWalla's reply may help.

use strict;
use warnings;

my @seq; # DNA sequence strings

for my $count (1 .. 4) {
    print "Please enter DNA sequence $count:";
    push @seq, scalar <STDIN>;
}

chomp @seq; # Remove line endings on all entries

printf "%2d: %s\n", length $_, $_ for  sort {length $a <=> length $b} 
+@seq;
[download]

Prints (for some arbitrary input):

Please enter DNA sequence 1:asdf
Please enter DNA sequence 2:zvasdfasf
Please enter DNA sequence 3:asd
Please enter DNA sequence 4:asdfasg
 3: asd
 4: asdf
 7: asdfasg
 9: zvasdfasf
[download]

You can visit PerlDoc to find out what scalar does.