Here are some cheap hotels in Oslo that will help you travel to Norway on a budget:
A centrally located hostel in Oslo. Prices go as low as 230 NOK for a bed in a 8-bed dorm.
Another centrally located, basic hotel. Cheapest room is 500 NOK for a single room with a shared bathroom and no TV and 720 NOK for a double room with shared bathroom and no TV. http://www.cochspensjonat.no/englishindex.html
If you’re planning on staying a little while in Oslo you can check out this website for short term/holiday apartment rental. Their aim is to offer accommodation at half the price of a hotel.
OvernattingOslo is a guesthouse with 64 furnished rooms. They offer rooms at very reasonable prices. Minimum stay is 3 nights. To check rates and availability or book a room go to: http://overnattingoslo.no/uk/