The "area" is a big one and these cities are not very close to each other. They form a big triangle. It's over 400 miles from Copenhagen to Stockholm, about 330 from Stockholm to Oslo and 380 from Oslo to Copenhagen. Whether you fly or take a train or a ferry, you will be spending a lot of time traveling. Now, it can be fun to see the scenery go by, but that may not be what you want to do, by land by sea or in the air.
Use Rome2rio to check out distances, see possible transportation options, travel durations and prices and maps of the routes. It's not perfect, but it will give an idea of how much would be too much for you.
I haven't been to Stockholm, but I've been to Copenhagen and Oslo and to Bergen with the famous Norway in a Nutshell trip thrown in. That is something you will not likely see anywhere else.
I think you could pick 2, but not do justice to 3. Copenhagen is the gateway unless you fly, but any 2 would be great.
Any time in Scandinavia will be very expensive and you will have to function in different versions of krone/krona/kroner in addition to EUR or whatever. The currency names sound almost the same, but they are not interchangeable, at least not without a fee.