One of the hardest things for a writer to do is write about the most serious questions of religion and philosophy and at the same time be funny. Høeg comes very close to pulling it off. At times the comedy gets a little pratfallish and relies too much on goofy names, but the book is consistently entertaining.
The story is a mystery of sorts, but not a whodunit, more like a how-are-they-going-to-do-it and how-can-they-be-stopped. It is a comedy in the classical sense, with youth vs. age, opening in confusion and ending in harmony. I don't think that gives away too much.