There are some discount airlines in Europe that might get you through one leg of the journey. Ryanair doesn’t offer direct flights, and I don’t think Europebyair will help you, but those are two examples of budget air options that don’t have an equivalent in the US.

I agree with the commenter above who said take the train and then two ferries – it’ll be among the cheapest routes anyway and you’ll get to see the world passing as you travel. If you do this, though, you’ll want to stop a couple of times on the way, because it’s hard to sleep on the ferries (unless you shell out extra for a cabin, and even then it’s not so easy). But by ferry, you end up seeing coastlines and passing islands in the early morning light, and that’s really special.