Does anyone have recommendations on best airlines and /or best websites to search for multiple one-way trips?

I will be leaving Washington DC mid-late October, spending about a week in Barcelona, and then going to Copenhagen for 2-3 days, then back to Washington DC.

Thank you!

Just go to www.kayak.com and choose the " multi-city" option at the top--it is called an open jaw itinerary.

Don't get separate one-way tickets. Search for open-jaw or "multi-city" flights, at least for the first and last legs of your trip. The middle part within Europe you can get separately or all on one ticket depending on the prices and availability.

Transvia.com fly between BCN and CPH. In October the one-way fare starts from around 75 euro.

Consider flying to a European hub airport then get onward flights from there. Most hub airports (with the notable exception of LHR) will have low costs flights to Barcelona, many will have flights to Copenhagen

I would try to book this with SAS. You can fly non-stop to CPH from DC. Book the flight DC-CPH-BCN-CPH-DC and look into booking CPH as a stop-over in either direction. That might end up being the cheapest option. Otherwise, as others said, book it DC-BCN/CPH-DC (or vice-versa) as an open-jaw. One-way trans-Atlantic tickets are usually quite expensive.

Otherwise, your options are Transavia, SAS/Spanair, or connecting for the flights between CPH and BCN. This is not a particularly well-served route.