One quick and easy way to assess popular and current styles for furniture and interiors in any city is to look at the department stores. Steen & Strøm on Kongengate is probably the most stylish store in Oslo with a beautiful interior but it concentrates on clothing and has what seems to be a deliberate approach to be generally international in style rather than specifically Norwegian.
Glas Magasinet on the square to the west of the cathedral is a more traditional store and has an extensive kitchenware department but again little seemed to come from Norway apart from an amazing display of blankets and a large display of fur and fleece.
As far as I could see, the general fashion in Oslo is not to buy Norwegian but German or Italian furniture. Stilverk on Kirkegata has a very good and carefully chosen selection of modern furniture but has no Norwegian pieces. Tannum Møbler, on Stortingsgata at the corner of Munkedamsveien, actually looks out towards the National Theatre and interconnects with Norway Design selling gifts from Norway and the shop has a beautiful selection of furniture but only one chair that is made in Norway ... the Scandia Chair designed by Hans Brattrud in 1957 and re-issued by Fjordfiesta.