The word for clean (verb) I usually see adjectives like 干净 and 清洁 for clean but I couldn't find a general verb for clean in Chinese. Let's say I want to say. "please clean your room before you leave". What's the right clean(verb) word to use in this sentence? And btw it will be really nice and helpful if you guys can provide some common "clean" verbs for different situations :D
清洁 can also be used as a verb "to clean", not just as an adjective
清理 is only really used as a verb "to clean" in general. It can also mean "to tidy up" (no water required), and even "to dispose of" (even euphemistically, like 处理).
洗 is used for "to wash", but where it overlaps with "to clean" is often in a construction with 给, e.g. 给X洗干净 "give X a (good/thorough) clean". 
清洗 is a more literary version of the above.
清涤 and 洗涤 are even more literary versions of the above, used in certain newspaper articles, official notices, translations of the Bible etc.
打扫 is used for "to sweep", but often gives the impression of "tidying up" and especially of rooms / parts of the house that don't require water for cleaning.
整理 is to "tidy up" or "arrange", and is also especially common for tidying up one's room.