Let us get this straight - it works when you create a link like this:
Her is a link [[sompäge]].
Does it work? Then everything is correctly configured.
Now on to your "problem". If you enter an non-ASCII char in the URL box you are in fact entering an invalid URL. This is because only 7bit ASCII is allowed in URLs. Because this is an invalid URL your Browser will probably try to be clever and will encode the the invalid characters (probably assuming them to be ISO8859-1) before sending them to the server. But because those character where encoded in the wrong charset, they will be decoded as some invalid chars on the DokuWiki side. DokuWiki then strips those chars.
I have no idea why it works with the DokuWiki-on-a-stick version - but it most probably not because of a different DokuWiki setting.