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First of all, this is an affirmative sentence: "I will do any work." I was trying to negate this sentence with "not" and "no". They are stated as follows:

I will not do any work.

I will not do any of the work.

I will do no work.

I think the first two sentences are OK, but the last one seems not so correct. I'm not sure about this so could you check them out for me and see if there's any problem with those sentences? Thank you very much!
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If I will do any work = I will do any kind of work available, then its absolute negation is I will not do any work = I will do no work.
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I think all the options you wrote are correct, the last one as well.
Please notice that though they all convey the same thing, there is still some difference in meaning.
the first two are pretty much the same:
the first means "I DO NOT INTEND TO DO ANY WORK" (there is no specific work).
the second - "I DO NOT INTEND TO DO ANY OF THE WORK [YOU GAVE ME]" meaning there is some certain work one need to do.
The last one on the other hand, is very strong "I will do no work". It doesn't matter which work, specific one or not.
It is correct to say it, but it sepends on the context.

I hope I've been help to you.
Luck!
Thanks, Anatbs. You're a great help to me, and so is Mister Micawber. Thank you!