There are 9 gyms in Kristiansand. There is 1 located in the city centre called Spenst and there is one in Sorlandsparken called Shapes. Prices vary with the memberships from 299 kroner per month to 600 kroner per month. The largest gym in Kristiansand is Spicheren. It is a student gym, but anyone can be a member. They have climbing, basketball and many other sports.
If you need a gym that is open 24 hours, then 24-7 fitness at Sorlandsparken is for you. When you join, you are given an access key so you can come and go as you please. Their membership is also one of the cheapest.
The gym in Lund is owned by an American who is a professional muscle coach and the Oxygo gym is at the Kristiansand football stadium.
Here is a list of the gyms in Kristiansand. If you click on the link for more information on the gym, it will take you to another website called Gymlink. This is Norway's gym portal.
Good luck!