You may be looking for something like this (if you only want data literally between the strings). Note the /s allows . to match newlines.

#!/usr/bin/perl

local $/;          # undef input record separator
my $str = <DATA>;  # get all file DATA into string

my @matches = $str =~ m!str1(.*?)str2!gs;
print @matches;

__DATA__
str1 Hello str2
str1 World str2
str1 ! str2
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