Obviously this is a very short list, just intended to be helpful, not in any way exhaustive.
Options are listed in order of rough order of price, from least to most expensive.
The only official youth hostel in Oslo. Not very centrally located, but not far from a T-Bane (Metro) station, on a line that goes directly to the Blindern campus.
Perminalen has private rooms and beds in shared dorms. It used to be for military personnel on leave. It is right in the centre of town.
These are for stays of three nights or more. For more than one person sharing these might be a good deal cheaper than a hotel.
A fairly cheap place to stay, in a nice part of the town centre.
Another possibility is a room at one of the Thon hotels. Thon is a big Norwegian hotel chain which has several branches in central Oslo.
Of their budget hotels in Oslo, the best location is probably the Thon Munch, right in the centre of town and convenient for a tram ride to the Blindern campus.
The Thon Astoria is also very central.
The Thon Spectrum is in a convenient, but somewhat down-at-heel part of the town centre, near the central railway station.
The Thon Gyldenløve is not a budget hotel, but is conveniently located in the west end of the city centre, and it is pleasant inside.
The Thon Hotel Europa is another midprice hotel, right in the city centre. Close to a stop for the 17 and 18 trams which go directly to the Blindern campus.