While I don't understand any foreign language well enough to follow an unfamiliar show that's not in English, I know many musicals well enough to enjoy them. It's also fun to listen to foreign cast albums; even if I can't understand all the words (or, in some cases like Hungarian, any of them), the spirit of a good performance comes through.
As you've already been told, American musicals, performed in German, are huge in Germany. Check what's playing in the cities you'll be in when you're there. The last time I was in Berlin, they had Rocky and King Kong, which didn't interest me. But on a prior trip I saw Rent and Cabaret, and I just missed Urinetown. And Cats ran almost as long in Hamburg as it did in London and New York.
Opera houses in Europe often do works that straddle the divide between opera and musical theater. For instance, I've seen Sweeney Todd in Barcelona at the Gran Teatre del Liceu (in Catalan), and in Berlin at the Komische Oper (in German).
Next to Normal was touring around the Netherlands the last time I was there, but the cities and dates didn't mesh well with my cities and dates (I would have had to take some VERY late trains to get back to my hotel). So, it's worth doing a bit of Googling for what's playing in areas you'll be, to see if you need to alter your travel dates and cities to mesh with the performances you want to see.
Not on your list, but both Paris and Madrid have a lot of theater; of course, it is mostly in French and Spanish respectively. However, just as Ms. Jo mentioned the English Theater of Frankfurt, there are English language theater companies in Paris, Vienna http://www.englishtheatre.at/ and other European cities. I saw Yazmin Reza's Art in Paris in English, which was an interesting "full circle" experience, since it started as a French play, then was translated into English and played London and New York (among lots of other places).