I am going to make a distinction between "unsolvable" and "invalid" Sudoku. A Sudoku is unsolvable if there is no way to fill in all the spaces without violating one of the rules of Sudoku. An Sudoku is invalid if the clues given violate one of the rules of Sudoku.
The minimum number of clues needed for a invalid Sudoku is obviously 2. However, I cannot figure how what is the minimum number of clues needed for an unsolvable Sudoku. I found an unsolvable Sudoku with 5 clues (shown below), but I cannot figure out how to proceed for here.
