I've fished in the Morrum River, in the Baltic, in the Archipelago, and in Finland. But all of this happened in two trips, so it wasn't as grand as it may sound.
Without going into a lot of detail, basically, only the ocean is open to fishing unless you've bought the rod rights to a particular stretch of river or water. You can go out with someone who has the right to fish, but it's definitely not like the U.S. However, the farther north you go, the more "open" water is available for everyone.
When I was at the Morrum, in the Laxhus area near the mouth, rod rights for the river were sold by beat, and the average cost was something like $200 a day with prices increasing by the desirability of the beat. But then, the Morrum is a famous river-- on its banks is the Abu Garcia factory. If you're in the area, stop by the company store-- you'll find some great deals there.
My guess is that in summer, the best fishing will either be in the archipelago area for pike, in some of the high lakes or for sea trout. The sea trout are sea-run browns. You might also catch sea-run rainbows, escapees from net pens.
One neat thing about Sweden is the "Everyman's Law" that gives everyone the right to wander where they will-- even on private property. However, as the Swedes say, "with rights come responsibilities", and you can't use the law to fish on someone's property.
If you haven't been to Sweden before, you'll be pleasantly surprised to find that in the cities everyone (or nearly so) speaks English. It's a mandatory second language in school.
It's a neat country to visit; I envy you the trip.
Keith