On a knife's edge

Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each. On both main diagonals digits do not repeat. Digits on an arrow sum to the digit in the circle from which the arrow emerges. Digits in a cage sum to the clue in the top left. Digits on a marked diagonal sum to the little killer clue outside the grid. A digit in a grey circle must be odd.