Let the first odd number be N1 = 2n+1, where n is any integer.
Then the remaining three, consecutive, odd numbers are:
N2 = 2n + 3
N3 = 2n + 5
N4 = 2n + 7
Adding together all the numbers,
N1 + N2 + N3 + N4 = (2n+1) + (2n+3) + (2n+5) + (2n+7) = 256
4*(2n) + (1 + 3 + 5 + 7) = 256
8n + 16 = 256
8n = 240
n = 30
The four numbers are: N1 = 61, N2 = 63, N3 = 65, N4 = 67