Below is an ever-expanding list of gluten-free restaurants in Oslo. some also have great vegan options. I myself am affected by coeliac disease and have been living in oslo for some time.
They offer gluten-free bread for their sandwiches and ask if you have celiac disease and the food preparation needs special treatment.
Joe & the Juice
Very tasty burger options that can be made gluten-free. They are well aware about celiac disease.
Døgnvill Burger
Another option in Oslo where you can get gluten-free and vegan burgers.
Munchies Munch Brygge - Oslo
A bakery with several stores in Oslo. They have a great selection of gluten-free baked goods.
Baker Hansen
A complete vegan restaurant with gluten-free options and a varying menu.
Nordvegan
Great place for people on a vegan and/or gluten-free diet.
OSLO RAW
Very good italian restaurant in Oslo. They have a lot of options for gluten-free pizza and pasta.