Clean up is used when something was actually dirty. Clear up, in this context, has the idea of putting things back in their place after being 'out' Neaten is used when things are already fairly well organized but not quite perfect Put in order, in this context, is to actually organize as well as clear up.. eg books not just on the shelves but in their right sections These are general differences for words that are often used interchangeably

The examples you've listed can be used in multiple ways, so giving a definitive explanation of each would be quite exhausting. edit: although I like Adam's reply as he's made a very good summary explanation of each. To me it would make more sense to compare two of them when used in a similar sentence, to outline the differences. For example, my interpretation in these two sentences which don't quite match the traditional meaning of cleaning and clearing: - I've cleared up my calendar = I've made room on my calendar to accommodate something else - I've cleaned up my calendar = I've removed some unnecessary meetings Sometimes a dictionary will end up giving you the best explanations of each, as well as some suggestions on other expressions that can be used instead of these. https://www.merriam-webster.com/dictionary/clear%20up https://www.merriam-webster.com/dictionary/clean https://www.merriam-webster.com/dictionary/neaten https://www.merriam-webster.com/dictionary/to%20order

"Clean up" can refer to cleaning a mess such as putting toys away, wiping a messy table area, etc. "Clean" (without up) us usually used in the USA when we talk about cleaning up something with soap or cleaning solution and water "clear up" could include acne on your face (fewer visible pimples), solve or clear up a misunderstanding, mucky water may be starting to clear up (be more see through), etc. "neaten" I have never heard or seen this word used before (I live in the USA). However, I would assume if I heard it that the person was talking about making something look neater. This could include a messy room, a messy paper (by erasing and writing more clearly), ect. "put in order" could mean to put things back where they belong, put them in better places so they are easier to find, put them in a specific order such as alphabetical or chronological, etc. The following are a few other similar words: Organize Tidy up Put away Again, my edit was only to fix my own typos.

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