I am sure there are many many more opportunites for fun with all three languages. Notwithstanding Monty Python's Hungarian phrase book sketch of course.
Well, there are opportunities for jokes mixing quite about any pair of languages, I suppose. A politically correct example is "I Vitelli Dei Romani Sono Belli" which in Italian reads like "Romans Calves Are Nice" and "Go, Vitellius, To The Sound Of War Of Roman Gods" in Latin. An XXX version involving German is "Kats In Der Kool" (not really sure is written correctly) which should translate in English like "Cat In The Coal", but also sounds like a very gross Italian expression.