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Non-Consecutive cages with entries in the right order (either ascending or descending). For the square cages they must begin at the top left and ascend or descend clockwise.

Available combinations
16(4) cage = {1357}
17(4) cage = {1358}
18(4) cage = {1359/1368}, no 2,4,7
19(4) cage = {1369/1468}, no 2,5,7
21(4) cage = {1479/2469}, no 3,5,8
22(4) cage = {1579/2479}, no 3,6,8

1. 16(4) cage at R1C8 = {1357}, locked for N3
1a. From order, ascending or descending, R12C8 = {17}, locked for C8, R12C9 = {35}, locked for C9

2. 17(4) cage at R4C7 = {1358}, locked for N6
2a. From order, ascending or descending, R12C7 = {18}, locked for C7, R12C8 = {35}, locked for C8
2b. 8 in N3 only in R3C89, locked for R3

3. 18(4) cage at R1C1 = {1359/1368}, 1,3 locked for N1
3a. From order, ascending or descending, 1 must be in R12C1, locked for C1 and N1, 3 must be in R12C2, locked for C2 and N1
3b. From order, ascending or descending, 5 or 6 must be in R12C2, no 5,6 in R12C1
3c. From order, ascending or descending, 8 or 9 must be in R12C1, no 8,9 in R12C2

4. 22(4) cage at R8C1 = {2479} (only remaining combination, cannot be {1579} because order, ascending or descending, would require 1 in R89C1), locked for N7
4a. From order, ascending or descending, R89C1 = {29}, locked for C1, R89C2 = {47}, locked for C2

5. 18(4) cage at R1C1 (step 3) = {1368} (only remaining combination), R12C1 = {18}, locked for C1 and N1, R12C2 = {36}, locked for C2 and N1

6. 1,3 in R3 only in R3C456, locked for N2
6a. 19(4) cage at R2C4 = {1369/1468}
6b. From order, ascending or descending, R3C4 = 1, R2C4 = {89}, R2C5 = 6, R3C5 = {34}

7. R2C2 = 3, placed for D\, R1C2 = 6, R1C1 = 8 (from order, ascending or descending), placed for D\, R2C1 = 1, R2C8 = 7, placed for D/, R2C9 = 5, R1C8 = 1, R1C9 = 3, placed for D/

8. R8C2 = 4, placed for D/, R8C1 = 2 (from order, ascending or descending), R9C1 = 9, placed for D/, R9C2 = 7

9. 21(4) cage at R8C8 = {2469}, (only remaining combination, cannot be {1479} because order, ascending or descending, would require 1 in R89C1) -> R8C8 = 9, placed for D\, R8C9 = 6, R9C9 = 4, placed for D\, R9C8 = 2
9a. R7C8 = 8, R7C9 = 1 (hidden single in N9)

10. R7C2 = 5, R7C3 = 6, placed for D/, R7C1 = 3, R7C7 = 7, placed for D\, R3C7 = 2, placed for D/, R3C2 = 9, R3C3 = 5, placed for D\, R3C9 = 8
10a. Naked pair {18} in R89C3, locked for C3

11. R6C7 = 6 (hidden single in C7), R6C8 = 4,

12. R5C5 = 1, R6C6 = 2, R4C4 = 6
12a. R45C7 = [18], R45C8 = [35] (from order, ascending or descending), R45C2 = [82], R4C6 = 5, R6C4 = 8
12b. R2C4 = 9, R3C5 = 3 (cage sum), R12C7 = [94], R2C6 = 8, R2C3 = 2

13. Naked pair {47} in R13C6, locked for C6 and N2 -> R7C6 = 9, R5C6 = 3

14. R7C6 = 9 -> R7C45 = [24] (from order, ascending or descending)

15. R6C8 = 4 -> R56C9 = [97] (from order, ascending or descending clockwise)

and the rest is naked singles, without using the diagonals.

I'll rate my walkthrough at Easy 1.0.