There are overnight ferries between Copenhagen and Oslo:

http://www.dfdsseaways.com/DSW/Intl/...ionCHO2006.htm

You can go by train, but it's an eight hour journey through three countries. To check your options, go to www.sj.se, click "In English" in the top-right corner and search for trains from "Köbenhavn H" to "Oslo S".

(Oh, great. The SJ search engine doesn't recognize "Copenhagen" if you type it into the "from" field - you get an error dialog that reminds you to type names in Swedish. However, if you try to type "Köpenhamn" instead, the same thing happens. Actually, you have to use the Danish name, "Köbenhavn". But in the search result page,
it's listed as "Copenhagen"...)