If you are looking for any type of flat water paddling, you don't have to look very far as there are bodies of water in very close proximity e.g. the Oslo fjord
As far as whitewater, I believe Kongsberg is the closest. It is about an hour west of Oslo. From what I understand they have several good playholes and they are in the process of building a wave.
Sjoa, which is about 3.5 hours north of Oslo is the Norwegian Mecca of whitewater. They hold the annual Sjoa River Festival in July. www.sjoariverfestival.no
Tyler Curtis lived in Norway during the paddling season for several years and should be able to provide you with all kinds of beta. You can contact him via his FB page: https://www.facebook.com/riverplay.ca