Kakuro is a game about sums, so to progress we need to check the sum of areas which are not necessarily just rows and columns. We also know that each sudoku row, column and block has a sum of 45. With some double counting we can deduce the sum of several 3-block areas:

The areas with sum 4 and 28 can only be filled with 1/2/1 and 9/8/9 respectively.

Next we look at 2 big areas. One time counting the sum of all the red areas and one time counting the sum of all the blue areas.

This gives us

sadly a contradiction. Even though the areas cover the same squares, red gives a sum of 545 while blue gives a sum of 550. This makes the puzzle unsolvable. Hopefully this is just a typo from the asker.

Kakuro is a game about sums, so to progress we need to check the sum of areas which are not necessarily just rows and columns. We also know that each sudoku row, column and block has a sum of 45. With some double counting we can deduce the sum of several 3-block areas:

The areas with sum 4 and 28 can only be filled with 1/2/1 and 9/8/9 respectively.

Next we look at a huge area. One time counting the sum of all the red areas and one time counting the sum of all the blue areas.

This gives us

sadly a contradiction. Even though the areas cover the same squares, red gives a sum of 545 while blue gives a sum of 550. This makes the puzzle unsolvable. Hopefully this is just a typo from the asker.

The typo was fixed and we can go on. My pictures still use the old grid including the typo. Filling in all the 3 block areas that have a sum of 4 or 26 gives us

Now we can solve some of the kakuro hints

Continuing to the left

Next we check the 6th sudoku row. The remaining tiles outside the sudoku have to have a sum of 6 which means the four squares have to be filled with 1/2/1/2.

That's all for now. Feel free to continue from this state, but remember that the typo from 28 to 23 is not fixed in my images.