Winter might be your best escape from LA. Norwegian Airlines is offering crazy-cheap deals during the off-peak travel period of mid-January through February, like roundtrip fares from Los Angeles to Oslo starting under $350. In addition, fares from Los Angeles to Copenhagen start around $360. A full list of discounted dates for Oslo can be found here, and for Copenhagen check here.
Beware that rates are subject to change, and can change by the minute, depending on how quick they sell. Norwegian offers cheap fares year-round, but these are extra cheap, and if you don't mind skipping a meal and traveling light, it's a great setup.
Although freezing-cold selfies may not be your exact vision of a European rendezvous, winter's still plenty beautiful in Norway. Plus, it's Europe for less than $500. Even if you don't wanna stay in Norway, you can bop around Europe with Scandinavian Eurorail pass, or even a $15 RyanAir flight to a tons of other places, too. And at this price point, you'd be crazy not to.