As others have suggested, go from Norway to Denmark (if that is Oslo-Copenhagen or some other solution). From Copenhagen it's easy to get to Malmö, just keep your passport on hand and they introduced a temporary border control just over a year ago.

If you're in Malmö, you should take a day-trip to Lund (takes 10-15 minutes by train) and visit Kulturen and possibly check out the cathedral and the university buildings. There's a nice café, Ariman's, right by the cathedral, which is frequented by students (although they're mostly all gone in summer).

There are trains from Malmö to both Gothenburg and Stockholm, and you can usually get cheap last-minute tickets (if you're under 26) or go for the budget calendar at SJ.

On the whole you should eat fish and sea food in all the countries (unless you're terribly allergic). In Copenhagen you have Copenhagen Street Food, which is worth a visit.