Square Odd Window Size just means that the filter window is square (N by N) and N is odd. N being odd ensures a well defined center to the window. 1D separable smoothing is a method used to implement 2D smoothing. It allows for you to smooth and image in O(M²N) time rather than O(M²N²) where M is the height and width of the image being smoothed.
If you do smoothing in the frequency domain using an FFT you can do this in O(M²log²(M) + N²log²(N)) which is an order of magnitude speed up if the smoothing filter is large.