1. I have just finished the work.

2. I just finished the work.
3. I finished the work just now.

(What about the use of 'just'? Are the sentences all grammatical and the same?)

They are all correct. Essentially, they are all the same.

The word, "just," means that you finished the work within the last few minutes or the last few hours.

Yes, all three sentences are grammatically correct, but they have slightly different nuances in meaning.

1. "I have just finished the work."
This sentence uses the present perfect tense and indicates that the speaker has finished the work very recently, possibly just a few moments ago. The word "just" emphasizes the immediacy of the completion.

2. "I just finished the work."
In this sentence, "just" is used as an adverb that means "a short time ago." It suggests that the completion of the work occurred recently, but it does not specify exactly when.

3. "I finished the work just now."
Similar to the previous sentence, "just now" indicates that the completion of the work happened only a short time ago. The difference here is that "just now" is used as an adverbial phrase at the end of the sentence, while in the second sentence, "just" is used as a standalone adverb.

So, while the sentences are similar in meaning, the placement of "just" and the use of "just now" can vary slightly in terms of the emphasis on the immediacy of the completion.