Would like to know how to ensure a cab right at the airports of all Scandinavian nations. What currency is accepted by the drivers in cash in all 4 capitals?
As at any other major airport, you can simply walk out of the terminal and catch a taxi. You can only expect the taxi drivers to accept local currency and it may even be difficult to get change for larger bills. In all Scandinavian countries, card payments are much too common for taxi drivers to have plenty of change.
At least in Oslo and Stockholm, you will arrive much faster and cheaper in the city centre if you go by train.