It's hard to say what you might mean by x, y, z here, but AFNI does keep a storage order in x,y and z. You can use 3dinfo to show the orientation
...
Data Axes Orientation:
first (x) = Right-to-Left
second (y) = Anterior-to-Posterior
third (z) = Inferior-to-Superior [-orient RAI]
R-to-L extent: -123.629 [R] -to- 115.434 [L] -step- 0.938 mm [256 voxels]
A-to-P extent: -145.970 [A] -to- 93.092 [P] -step- 0.938 mm [256 voxels]
I-to-S extent: -42.147
-to- 61.853 [S] -step- 2.600 mm [ 41 voxels ]
...
Here the definition of x,y,z is fairly clear. X goes from right to left, Y is anterior to posterior, and Z is inferior to superior. All go from negative to positive depending where the 0,0,0 is set. The orient code is set to the first letters of each of the starting directions, i.e. RAI.