Getting a hotel in Oslo can potentially be difficult. In peak periods, when big fairs or conferences visit Oslo, tourists have been sent as far as Lillehammer (170 kms, 2h 15 min by train) to find accommodation. It would be smart to reserve a room in advance. There are also relatively few youth hostels, etc., for backpackers and people travelling on a budget. During Nobel Prize week room availability will fall and prices may double.
Budget
Camping
Bogstad Camping, + kms out of town at the entrance of picturesque Sřrkedalen (T-bane 2 to Rřa, then bus 32, 41 or 47 to Bogstad Camping or Peder Ankers plass). Bogstad has cabins as well as tent space. edit
Ekeberg Camping, (Bus 34, 46 or 74 to Ekeberg Camping. The trip takes 10 minutes from Central Station.), . checkin: 7.30 AM to 11.00 PM. Open June 1- September 1. The closest campsite to central Oslo. Beautiful view of the city. No cabins. Owned by the Norwegian Automobile Federation. Mini-golf and horse rental. Fully equipped sanitary facilities: showers with hot and cold water, toilets, kitchen, launderette. 4-person tent: NOK 260. edit
Langřyene Island, (take ferry 94 from Vippetangen). Not an official campsite; however, Langřyene Island is the only Oslo fjord that allows free camping (tents only). You may only stay 2 days unless you have special permission. You must keep the island clean. Police have their own boats and enforce these laws via hefty fines. Free!. edit
Oslo Fjord Camping, 8km south of Oslo central station (Train to Hauketo, then corresponding bus 76 to Hvervenbukta, or bus 87 (both options summer only)), . Near the beautiful swimming spot of Hvervenbukta. 2-person tent: NOK 150; 4-person tent: NOK 200.