SAS has round-trip flights from Chicago (ORD) to Berlin (BER) for $388-$413 with a connection. Flights March, April, May, August, September, and October. Departures on Tuesday, Wednesday, Thursday, and Sunday. Very few extended weekends available.
Carry on bag with a maximum weight of 18 lbs is allowed for free on SAS. You can avoid seat selection fees by accepting the randomly assigned seat at the gate. Upgrading to a higher fare class that includes a full-size carry-on bag for $28 may be cheaper than booking the discount fare with the added carry-on bag fee (for about $60).