"I have finished the work" could mean either one. It implies nothing about when the work was finished. In practice, we might use it a little more often to mean something like situation #1.
The reason for this is that the present perfect, have finished, relates the past event to the present. For example, my friend might ask, "When will you finish writing your book?" and I might answer "I have finished it!" meaning that as of now, I have finished writing my book. But that doesn't mean I just finished it now; I might have finished it six months ago.
If I were reporting to my boss that I had finished the work he had assigned me, I would probably say, "I have finished the work." It would be grammatically correct and understandable to use the simple past, "I finished the work", but using "have finished" emphasizes as of right now.