Hiring Process in Norway for Postdocs
I see that the question is old, and hopefully, you have already started in your position. However, I will try to answer anyway for the benefit of others.

I was previously employed at a Norwegian university as a PhD student. The slowness you describe is sadly very familiar.

When I received offers for PhD positions (~5 years ago), I did get formal letters like you describe, but in some cases more informal contact forms were used to speed up the process. The deadline for me to respond to these formal offers was two weeks. As have been mentioned in the comments there may be some administrative overhead in between the candidates. I do not know for sure, but having observed how slow administrative units can move at Norwegian universities, I wouldn't be surprised if the overhead is substantial.

The best way to speed the process up is to find someone at the university that is interested in someone -- you -- starting in the position as soon as possible. Typically, this will be the professor you will be working for. This professor can then push the administration to work faster and contact the people ahead of you on the ranking list to kindly ask them to withdraw their applications, seeing as they already have accepted another position anyway. As there is no need to send formal offers to people who have withdrawn their applications, this last part can speed up the process tremendously. If you can't get a professor involved in your case, trying someone in the university administration can also be effective (but it is my impression that it is harder to get the administration involved).