Sunday August 25 train from Copenhagen to Kalmar Sweden
You have two options, Öresundståg direct or high speed train to Alvesta and change there to a local or regional train. The former has a fixed price, buy the latter in advance at www.sj.se
Tuesday August 27 train from Kalmar to Stockholm
Buy in advance at www.sj.se. Note that Kalmar to Stockholm requires a change and you have a choice of two routes, with a change in Alvesta or a change in Linköping. In my opinion the route via Linköping is a bit more charming and more scenic, even if it's often a bit (15-30 minutes or so) slower. If you can't see any options that include a change in Linköping, add Hultsfred as a via-station.
Friday August 30 train from Stockholm to Oslo
Buy in advance at www.sj.se
Monday Sept 2 train from Oslo to Bergen-Norway in a Nutshell
Follow the advice above, acraven knows what they're talking about. And yes, I agree that two days in Stockholm is a very short visit.
I suggest you cut down on Oslo. The Viking Museum is closed until 2027
and there's just not much else there. One night is enough.
Au contraire, there is a lot to see and do in Oslo. If you think the Viking museum is the only thing worth visiting I can really recommend a trip to Oslo because you've missed a lot.