As far as I can tell I shouldn't be using ÅÄÖ (somthing like they have no visual representation in ASCII??).
So what is considered more SEO friendly? Replacing i.e. all "ä" with "a" or "ae"? (The CMS Umbraco replaces with ae and I'm leaning towards this).
EDIT: Summary of how some Swedish sites does it:
aftonbladet.se/ ä => a (http://www.aftonbladet.se/kropphalsa/)
uppsatser.se/ ä => ä (http://www.uppsatser.se/om/v%C3%A5rd+av/)
lindqvist.com/ ä => a (http://www.lindqvist.com/b/google-maps-placering-ar-gratis)
umbraco CMS sites (like vaxab.se) ä => ae (http://vaxab.se/tjaenster.aspx)
dn.se/ ä => a (http://www.dn.se/sthlm/brak-utanfor-aspuddsbadet-1.1008899)