Is there any differences in usage between Klausur, Prüfung, Examen, Test*, and (Klassen)arbeit*?
* Edit: added more synonyms based on answers below.
Let me go through each of them to explain some differences:
Prüfung: The most generic term of all three. A "Klausur" is a kind of "Prüfung", as well as an "Examen".
Examen: This term is in modern times used only with final exams within some educations, especially when the test is conducted by a state authority. Then it is called "Staatsexamen"; examples for this might include final exams for law or medical students. This Wikipedia article lists other examples for "Staatsexamen". If I understand right, "Examen" was once used for every type of (final) exam in higher education.
Klausur:: A written test in universities. The term sometimes* is used for written tests within the last two years of grammar school (Oberstufe).
[*]: At least when I was in grammar school...
AFAIK, Klausur and Examen¹ are only used for theoretical tests, while Prüfung can as well be a practical test, like Führerscheinprüfung (test for driving license) and Materialprüfung.
You couldn't say Materialexamen or Materialklausur. (Well - in German, you're free to combine old words to new ones, so you could say it, but people would raise they eyebrows for this unusual combination).
Test would be another alternative, which is used for practical tests too.
Klausur has a second meaning as in "Die CSU geht in Wildbadkreuth in Klausur.", which means conclave, and similar: enclosure.
¹) according to Wikipedia (thanks to Hendrik Vogt), Examen is used, for example for musicians, for practical tests too.
Just want to add the word "Arbeit". At the school I visited, we only used the words "Prüfung" and "Arbeit". We used "Prüfung" for the "final exams" and "Arbeit" for the normal tests.
Schreiben wir morgen eine Arbeit in Deutsch?
"Prüfung" could be most generally translated as "test".
An oral test, could be a "Mündliche Prüfung", for instance, but there is never a "Mündliche Klausur". It wouldn't make sense, since the word 'Klausur' implies a silent session behind closed doors.
"Examen" implies almost every time a kind of final test, final exam, etc.