I notice that you have global $x appearing again in the code of readstring(). That will replace $x whenever readstring is called, whether or not you assign to it. Declaring the lexical my $x = <<EOF; in the first line of the sub will fix that.

You can do without temporary variables entirely with the following oddity,

sub readstring () {
    <<'EOF';

here is my unquoted
multiline string

EOF
}
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The empty prototype is a hint to the compiler that readstring returns a constant value and can be evaluated during compilation. I single-quoted the heredoc end tag to emphasize that there is no variable interpolation to happen. ("unquoted" is only true in a typographic sense - heredocs can employ any of perl's flavors of quoting)