1/ Finally is the same as lastly. It introduces the last element in a series.
Ex: We must increase productivity. We must reduce unemployment. And finally, we must compete in world markets.
Finally can also suggest that one has been waiting a long time for something.
Ex: She has finally got a job.
2/ At last suggests the idea of impatience or inconvenience resulting from a long wait or delay.
Ex1: She has passed her exams at last.
Ex2: When at last they found him he was dead.
3/ In the end suggests that something happens after a lot of changes or uncertainty.
Ex: We made ten different plans for our holiday, but in the end we went to Goa again.