exactly. "work" has several meanings, but the meaning of "job/effort" is an uncountable noun, so it doesn't have a plural. this is actually invalid English
I mean you do see it in cases like "road works" or "fireworks" or "works of art". In the sentence given above they're asking for plurality and naturally "works" would be that even though you'd generally only say "doing work etc".
You still never see work pluralised unless it is coupled with a few specific nouns. The plural of work is still work.
That is not fully accurate. "the works" - 'the' is not a noun. "Works of art" - 'of art' is not a noun. "Works in process" - you would not say "work in processes", you instead pluralize work to works.
'Work' has more of an abstract meaning, like teaching or furniture - but that does not mean you can't or don't pluralize them. Teaching is an important job; the teachings of Jesus Christ, etc.
The only time I've ever heard people say "works" (when they're referring to jobs or tasks) is if they're a non-native English speaker. I've heard this from native German, Chinese, and Japanese speakers, but never from a native English speaker, because the only time "work" is countable is in "work of art".
Roadworks is not really plural, it's just one word. You can't say 5 roadworks, for example.
Fireworks can be plural (if you're talking about the device itself) but again, it's still one word.
I cant think of a context where this would be lexically and grammatically correct. Should be 'tasks'
We can't think of a context because there isn't one! The use of "works" is wrong. Period.
Here we have to translate a Vietnamese sentence into an incorrect English sentence. There are a few specific situations where the plural "works" is used. This sentence is not one of them. "They do necessary work" is correct. "Necessary works" is incorrect.