EuroBonus makes most sense if you're living in Scandinavia as it's the 'home' airline. Be sure you accrue EB miles when you fly the other Star Alliance airlines, CO/UA, US Airways, Lufthansa, etc.
In addition to the direct flights from CPH to EWR/ORD/IAD on SK, with onward connections on CO/UA partners, you can also fly with CO out of CPH to EWR. If you are traveling CPH-MCO on occasion, LH has a very good connection through Frankfurt (CPH-FRA-MCO) with the return flight leaving MCO late in the evening, which I quite like when I'm returning from the U.S.
I agree with SK_RSJ that you may want to drop IcelandAir in favour of the *A partners. While they have some decent fares and connections, and a painless airport to navigate, the flying experience isn't that great.
If you're trying to avoid CDG, that shouldn't be a problem if you stick with *A because AirFrance is a member of SkyTeam. I've been flying CPH to the U.S. with DL/SkyTeam for some years now, but they've dropped their CPH-JFK and CPH-ATL routes to just a CPH-JFK seasonal (summer only) which makes it less attractive to fly SkyTeam now (needing to connect in AMS or CDG).
Another *A partner is AirCanada who has a direct flight from CPH-YYZ (Toronto). That might sometimes be an option for you with connections to the US from Toronto.
Lastly, keep your eye on the Virgin-Atlantic (VS) discussions about the possibility of their joining Star Alliance. If that happens, there could be some good connections from CPH to LHR/LGW/MAN with SK or BMI onward with VS to the U.S. (including BOS/EWR/JFK/MCO).
Susan