> If Sweden isn't part of NATO, would it be correct to call Sweden and the US allies? I don't see it.

Sweden and Finland signed a "Host Nation Support Agreement"[1] with NATO a few years ago. And there's also been previous joint military exercises with the US/NATO in Sweden, and the upcoming exercise "Aurora 17"[2].

[1]http://shape.nato.int/finland-and-sweden-signing-a-memorandu...

[2]http://www.forsvarsmakten.se/en/activities/exercises/aurora-...