I am certainly not the authority on economics, but if EUR falls relative to SEK, then in Sweden imports would be high, exports would be low. This in turn would effect local manufacturers because people would prefer buying things from outside for lower price rather than within country for higher price. This might lead to closing of manufacturing units in Sweden and loss of jobs in the country.
Also, wages would decrease relative to the rest of Europe because SEK is more valuable now (This would also result is movement of jobs out of Sweden to other European countries).
Now the imports are flourishing and export industry is dying out and wages are getting lower, unemployment may be rising. The in-country manufacturers would keep the prices same for their goods to be sold within the country, but people's wages has decreased, so in order to compete with competitive import industry they will reduce the goods prices, which in turn will decrease their staff's pay.
Thus, even though SEK is strong compared to rest of Europe, but within Sweden, people are making less than before, which in turn will lead to inflation.
Also, I haven't yet accounted to another possible consequence of this, while SEK is stronger relative to Euro and Swedes might be making less money, American economy might not be affected and $ would still be the same. This will affect Swedes international buying power.
A strong control by government may change a few factors here. If I am wrong somewhere, I would be happy to be learn new things, please give reasons.