Out of curiosity. What is your flight schedule? The EWR flight from CPH leaves around 10:25. From OSL it's 11:10 and from ARN it's 12:25. MXP-OSL is a 5 hour trip with a layover of about 1 hour in CPH and OSL. So to make the 11:10 flight in OSL you will have to leave at 6am from MXP and to my knowledge SK do not have such an early flight from MXP.
The other option MXP-OSL-CPH-EWR with the late CPH-EWR flight doesn't work either as far as I know.
But as Tango Alpha wrote. I won't worry about the luggage unless you have something real valuable in it or really need it when you arrive at EWR.