I think that the confusion of dealing with obliquity is that AFNI really only handles cardinal data. While the initial data may have a transformation matrix that defines the transformation from the ijk storage indices to real world xyz coordinates, the AFNI display and almost all processing assumes the data lies in grid that corresponds to the closest cardinal equivalent orientation (RAI,LPI,...).

The 3dWarp commands transform the data so that the data becomes cardinal in a cardinal grid or oblique, but still in a cardinal grid by tilting the rectangular prism of the original data into a grid with zeros outside the original data. In both cases, the data doesn't really really need to be labeled as oblique. In the end, if you have aligned your datasets to match with either the oblique->cardinal or cardinal->oblique transformation, you should be okay.