I chose Oliver Finnegan. I might have chosen Maxwell because Max is a great nickname, but I really don't like it paired with Elias (because Maxwell ends with the same sound Elias begins with). Also, Oliver Ray sounds far better than Max Ray (which sounds a bit like a cartoon weapon or villain). That said, the -er kind of blurs into Ray... Oliveray. Still a better choice than Flynn, though!
Thank you all for your honest thoughts! Keep the votes coming :)
Those are all quite nice names, but I ended up voting for Oliver. Oliver and Finnegan work together in a very unique, kinda spunky way. Finnegan makes Oliver more fun. Flynn I like, but the whole flow of the three names just doesn't work that wonderfully. Maxwell would be my second choice, and it does go well with Elias, but not quite as awesome as Oliver Finnegan.