I created a sub-sub-level page with the name "Nøsting" and all seemed good. I published the page as normal, it showed up in the menu bar as a drop-drop-down, but when I clicked on it Firefox reported that the page could not be found.
I went back to editing the page in the WP Dashboard and noticed the "ø" was not appearing happily in the slug so substituted a plain lowercase "o" and suddenly the page could be found and loaded normally.
I now notice that the Permalink appears as: "http://www.hatchtown.com/tools/misc-tools/nosting"
So, I'm VERY happy! At the top of the page AND on the dropdown menu the title still shows as "Nøsty", but it's plain "nosty" behind the scenes.
I will be happier if I understand what characters are allowed / not allowed and what are the workarounds for using them.