Odd Solution
For the odd difference solution, the pattern you have to do is: odd, even, odd, even. The reason is, because you only have four evens and fie odds. you have to taken away an odd from an even to get an even difference. you have to put one in each corner and then one in the middle.
Even Solution
The even difference in the grid is nearly possible, but actually impossible. The reason being, because you only have for evens and five odds. You have to take an odd from an odd too get an even difference. the you have to take an even from an even to get an odd difference. You cant put the numbers in the grid without getting an odd difference
The general statement I have to make, is that an odd take an odd is an even answer. Even take an even is even. Odd take even is an odd answer.