I'm writing book(sort of, it's really a series of journal entries by fictional people) where a king weds a Nordic princess for strategic advantage. What sort of advantages would a king get if he married a Nordic princess?
The Medieval era is long and had a lot of different effects on the Nordic countries. Could you specify a bit more?
For example, the Danish peasants slipped into serfdom during this era, especially during the Danish interregnum 1332–1340, while their Swedish brethren became increasingly hostile and willing to defend their own political and economical rights with arms in hands and did so well at several occasions.
Dried cod and salted herring, from Norway and Denmark respectively were attractive trade goods as they were long-lasting food that could be consumed during catholic lent and thus an income source to tax for the monarch of the respective country.
Sweden provided much of the really long lumber needed for some of the cathedral construction in catholic Europe during the era. In general, Sweden (and Finland, then part of Sweden) provided much of the tar, hemp (for rope) and lumber used by the Hansa and the nascent Dutch traders for their ships during this era.
Denmark secured firm control of the Danish straits and built the castles as Helsinborg and Helsingör to control it and be able to extract tolls on all trade going in and out of the Baltic Sea. This provided the Danish monarchy with a source of real coin in an era where a lot of taxes were paid in perishable goods such as grain, cattle, furs and so on. This gave the Danish monarchs the ability to hire Frisian and Low German mercenaries, often knights and landsknecht.
During the 15th century, the Sala silver mine in Sweden was at its most productive, and provided a steady flow of silver.
The problem for your scenario is that the centralisation and royla power of the Scandinavian countries varied wildly during the era, and the Black Death crippled all three societies - in Norway it eradicated the nobility as a social class. Denmark had its interregnum and expansion of noble power, Sweden had the personal crusade of Bo Jonsson (Grip) against royal power, all of which resulted in the Kalmar Union and then the clusterfuck of a civil war it was for the later 3/4 of its existence.