Bus,ferry,train,plane

I would like to know, if there any sort of direct transportation to
Stockholm or transfer to other place to get to Stockholm from
Copenhagen airport?

There are direct trains from the airport to Stockholm, and many more options with a change in Malmö. Buy the tickets at www.sj.se

From Stockholm to Oslo what kind of transportation is better and
cheaper cuz Scandinavian countries are pricey?

The train, buy the tickets a month or two in advance at www.sj.se

From Oslo to Copenhagen same as second question.

The cheapest option is probably the overnight ferry. It also gives you some nice views.

The distance between the cities is 657 km, and buses make the trip in just under 6 hours.

You can fly to Stockholm in about 1 hour, however the airfares are relatively expensive @ $267 Euros to $289 Euros. One alternative might be to take Norwegian Air Shuttle (seasonal flights) into Oslo or Helsinki and see if they have a corresponding connecting flight back to Stockholm.

One alternative might be to take Norwegian Air Shuttle (seasonal
flights) into Oslo or Helsinki and see if they have a corresponding
connecting flight back to Stockholm.

That sounds like a lot of faff compared to just taking the train to Stockholm.

Just booked train from Copenhagen airport with a transfer in Malmo for Stockholm, Stockholm to Oslo aslo with train and finally I was amazed for a price for night ferry from Oslo to Copenhagen just 70€

Good luck! I hope you have a nice trip!