Perl needs to know that you are dealing with Unicode characters. Consider:

#!/usr/bin/perl
use strict;
use warnings;
use utf8;

my $str = "ö123
å456
å789";

open my $inFileUTF, '<:utf8', \$str;

my @lines = <$inFileUTF>;
chomp @lines;
@lines = map {scalar reverse} @lines;
print "Using utf8\n";
print "$_\n" for @lines;

open my $inFile, '<', \$str;

@lines = <$inFile>;
chomp @lines;
@lines = map {scalar reverse} @lines;
print "\nUsing default file I/O\n";
print "$_\n" for @lines;
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Prints:

Using utf8
321ö
654å
987å

Using default file I/O
321¶Ã
654¥Ã
987¥Ã
[download]

Note the use of both strict and warnings. Always use strictures.

Note the use of three parameter open and lexical file handles (usual file checking omitted because of the string trick).

The \$str syntax lets me open the string as though it were a file. Very useful here to provide the data in the same "file" as the script.

See PerlIO for a description of the open custom layer options - the :utf8 bit.