Summer of course is the peak, most extortionally priced time to go from the US to Europe. If you want the absolutely lowest fares, you'll want to open up your strategies.
(0) If you're not flexible with dates, your options are next to nil.
(1) Consider two separate tickets and do fancy shuffling between airlines and terminals at some intermediate point. For example, one round-trip Chicago-Dublin, and a second round-trip of Dublin-somewhere else.
(2) See what's on sale. For example, New York-London may have huge competition, price-matching deals, Get a second ticket to go the rest of the way.
(3) Discount airlines like Air Berlin or Condor have crazy one-way deals on specific days of the week. Your challenge is to get to/from the gateway that they serve. Polish LOT also has some interesting deals.
(4) Europe has many low-budget airlines like Easyjet and Ryanair. Your challenge again is to get to/from the airports they serve.
(5) Depending on what you're willing to tolerate, Aeroflot may have some deals.