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

while (<DATA>) {
    my $remove_new_line = /string1/ .. /string2/;
    chomp if $remove_new_line
          and 0 > index $remove_new_line, 'E'; # not the last line
    print;
}

__DATA__
x
y
z
string1
a
b
c
string2
1
2
3

##</code><code>##

x
y
z
string1abcstring2
1
2
3