First off what I am posting is not based on my own personal experience since my trip to Oslo is not until this July. That being stated, a destination's food is one of the main reasons why my wife and I decide where to travel and what follows are some recommendations based on several TV programs I have watched about the cuisine in Oslo that helped us decide that Oslo was worth the visit.. So here goes.
According to one source, Oslo is "coffee crazy" with the Tim Wendelboe Cafe being a great place to get what Norwegians consider great coffee. The Gamle Raadhus serves reindeer steak which, even by Norwegian standards, is an expensive night out but where else can you eat reindeer? Vaaghals serves up "vafler" or Norwegian waffles - quite a stack with strawberries and, odd by American standards, the national cheese spread on it too. Mathallen is an international food hall that has so many interesting places and different types of foods that my week in Oslo may not be long enough to sample them all.
All of these places have their own websites and, if you like, I can let you know the programs I watched to learn about these places. I hope this helps. Please let me know if you visit any of these. Enjoy your trip!