What is the work you can't not do?
This might depend on context, but probably means "What is the work that you must do?" The sentence makes me think of a stressed student or employee who has too many tasks and a friend is trying to help them decide what has to be done and what can wait or be forgotten about. This is a grammatical sentence that would not be used in a formal sentence but would be said by a native speaker.
What is the work you can't not to do?
This sentence is not correct English. Root forms of verbs (to do, to be, to eat, to dance, etc.) cannot be used in this way. Since the sentence shows that the second person "you" is the one doing or not doing the work, the verb "to do" must be conjugated for the second person. This is not a grammatical sentence that would not be used by a native speaker.
What is the work you can not do? (or What is the work you cannot do?)
This is a fine English sentence, but it does not have the same meaning as the first one. Instead, this question asks "you" what tasks they are not able to do. Maybe a student cannot complete their homework because they don't understand the problem. Maybe an artist cannot continue painting because they do not have the correct paint. This is a grammatical sentence that could be used in a formal sentence and could be said by a native speaker. However, this sentence sounds awkward to me. I would likely say "What work are you not able to do?" instead.
What the work is you can not do?
What the work is you can't not do?
Both of these are not correct because they are missing a verb between the adjective "what" and the article "the." English does not always need articles. For example, in my previous sentence, the phrase "What work are you not able to do?" is okay and even sounds more natural than "What is the work..." However, if you have a question word + article + noun, then you also need a verb. Here are some more examples:
When is the concert?
Who is the singer?
How late does the concert last?
Why is there a dog on the stage?
Who is yelling "fire?"
Where is an emergency exit?
Who gave you that gift?
What color is it?
What gift did you get for your sister?
When the concert?
Where an emergency exit?
Who the singer?
I hope this helps you!