use utf8 affects string literals in the source (and STDIN and STDOUT?). Strings stored in a data file won't be affected by it.

Simply specify the encoding of the data file when opening the data file.

open(my $fh, '<:encoding(UTF-8)', $language_qfn) or die;
while (<$fh>) {
   ...
}
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If the you have a handle and not a file name, use binmode.

binmode(STDIN, ':encoding(UTF-8)');
while (<STDIN>) {
   ...
}
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Or decode the string explicitly

use Encode qw( decode );

open(my $fh, '<', $language_qfn) or die;
while (<$fh>) {
   $_ = decode('UTF-8', $_);
   ...
}
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Output is very similar. Set the encoding on the output handle or use encode.

open(my $fh, '>:encoding(UTF-8)', $output_fqn) or die;
print $fh ($text);
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binmode(STDOUT, ':encoding(UTF-8)');
print($text);
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use Encode qw( encode );
open(my $fh, '>', $output_fqn) or die;
print $fh (encode('UTF-8', $text));
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Update: Added output info.

(and STDIN and STDOUT?)

It doesn't. For that you need use open qw/:utf8 :std/;

The separate file is a perl file such as:-

$stringhello = 'Hello';
$stringlogin = 'Login';...
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that's brought in with require lang.pl; I was referring to adding use utf8; to the top of that file. Wouldn't that do the same?

Yes. It can even be in other encodings using use encoding '...';.

You still need to handle the output, though. The strings of characters need to encoded into strings of bytes using one of the methods I posted.

Sure there is one: Locale-Maketext. Take a look at the author's article on TPJ about software localization: Locale::Maketext::TPJ13.