Something else may be going wrong, as this works:

#!/usr/bin/perl
use strict;
use warnings;
while (<DATA>) {
  print if /string1/../string2/;
}
close DATA;
1;
__DATA__
 this is string0 line
 and this is string1 line
 this might be string1a line
     and this line has string2
 to finish, string3 line ends it all
[download]

produces output

 and this is string1 line
 this might be string1a line
     and this line has string2

Note that sometimes people use the __DATA__ feature to show file I/O related code. Please don't let that confuse you.