Every newcomer to Norway faces the same issue. You have to carry passport around with you. Passport is too big, doesn’t fit pockets (especially during summer). Passport is travel document which we should store safely until need for traveling. It would be much convenient to have credit card sized photo id.
Your residence permit (oppholdstillatelse) is not valid photo id. Yes it has a photo of you, but it is not a photo id. It is actually only valid in front officials if presented together with other valid photo id document. Banks used to issue personalized payment cards to foreigners before. Those cards had small picture and signature behind. But not anymore. Since 2014, there was less and less cases of foreigners getting them in small banks. I am not aware that anyone got it recently. Drivers license is valid photo id, but most of us have to convert them or even to pass exam all over again. And in Norway that is significant cost, which comes after settling and finding your way around (for which you often need photo id).
Every person born before 1. January 1985 can get moped license of AM class issued without having to pass theory or practical test. What you need to do is fill in the request form at Vegvesen (Norwegian Public Roads Authority) office. There on the spot there is a check do you see good enough, and your general health questionably. Then you pay the fee that is kr.280 and kr.75 for the photo. After a week, you will get your drivers license in the mail. Voila, there is your photo id, plastic in credit card size (plus you can ride a moped).
This lifehack is legal and works. I have personally identified myself with such AM license to a police officer when I was taking my B drivers license exam.
If you are younger than 1. January 1985 sorry but your passport is the only option I know of.
I don’t guarantee this will be valid forever.
If you find out anything changed, let me know.