While in Oslo, dont miss Gustav Vigelands park, this is amazing, and I visit it every time Im in Oslo. Also dont miss the Heyerdahl museum, which is quite unique (even more if you know this man). Polarship Fram is also worth visiting, and the Skanzen too. This all can be fit into a day, and I found it quite interesting.
Nature is the best in Norway, hands down. If you dont want to travel up nort, but wanna see some real nordic landscape, go to Hardangervidda and do some trekking there (circumnavigating Hardangejökull is highly recommended, but for the more experienced. Takes 3 days.) Or go to Stavanger, then by ferry to Lysebotn, see the mighty Kjerag, go up tho Preskestolen (?) then go overland back to Oslo.
Also there is a touristy thing, called Norway in a Nutshell or something. This takes you from Oslo by train through Hardangervidda, then an other, steep train takes you down to a fjord, then you board a ship, then you board a bus , then a train again, cramped with real touristy tourist, some pretty girls, and lots of camera-clicking. BUT if you have like a couple of days for Norway, this trip however commercial, shows a rough overview of how the other parts you can not see look like.
About travelling: I recommend hitchhiking. Norwegian people were always exremly friendly to me, I did not have to wait much for a ride in any place of the country. I hitchhiked many thousands of kms in Norway, sometimes packed with 70kgs of climbing gear, but it did not matter, I met many memorable people, and get to know so much about the country otherwise I couldnt have.