This works as expected for me:
alert("æøå");
... creates an alert containing the string "æøå" whereas
alert("æøå");
... creates an alert with the non-ascii characters.
Javascript is pretty utf-8 clean and doesn't tend to put obstacles in your way.
Maybe you're putting this on a web server that serves it as ISO-8859-1? If you use Apache, in your Apache config file (or in .httaccess, if you can override), you should have a line
AddCharset utf-8 .js
(Note: edited to escape the ampersands... otherwise it didn't make sense.)