Thankfully, it was much easier than I thought! Here's what solved my problem:

#!/usr/bin/perl -w
use strict;
use Encode qw(from_to);
use Encode::Byte;

my $file = "C:\\Αντίγραφο
+\\VOLINFO.TXT";
from_to($file, "utf8", "cp1253");

open FILE, $file or die "can't open $file: $!";
while (<FILE>) {
    print;
}
close FILE;
[download]

I can't understand why it didn't work when I directly used this type of characters: \xc1\xed... etc. (I checked! The output was correct cp1253 characters... or wasn't it?)

Oh well, I guess that's why some people write modules that work while I get stuck with encoding issues before even writing a line of code. ;-)

Anyway, thanks to everybody who took the time to help me out.