Hi okflyer,
What is your itiniary? Do you have many domestic segments?
Generally you will be allowed to go by the "piece" system on the domestic/intra-scandinavian segments directly following the intercontinental hop, hence on SEA-CPH-OSL and SEA-CPH-BGO you have the full allowance all the way.
Next question is if you have status with any *A carrier. If you are Eurobonus Silver that gives you an extra 10kg, all *G cards give 20kg extra. Note that the allowance in Europe in Economy is 20kg in total. You may check two bags, hence once all the gifts are handed out you might be ok.
Oh, and if you have no status, how many points have you earned on EB this year? Flying intercontinentally gives you a lot of points, so you might end up becoming EBS enroute. (With 2 r/t you will for sure be EBS upon your return to SEA, but if you got it earlier it would make life easier.)
Not knowing your route of travel it is a bit hard to give advice, but one idea would be to leave one suitcase behind at OSL in the luggage storage facility.