I'm a bit confused by which dataset is or isn't aligned to what. The NIFTI header contains the transformation matrix that describes the coordinate system of the data. You can see the transformation matrices with

nifti_tool -disp_nim -infiles dset.nii |grep to_xyz

These lines describe two representations (q-form and s-form) of the transformation matrix in the NIFTI header. The first three elements of each row will contain only one non-zero element if the data is cardinal (not oblique).

By default, AFNI will use the closest cardinal matrix and use that for definition for its display. You can try to get around this by using 3dcopy to copy the data to AFNI format and then changing the determined cardinal orientation with 3drefit.

But if at least one of your datasets is oblique, so you might want to transform the other datasets to match that obliquity. Use 3dWarp -card2oblique or -oblique2card depending on what's going on with your data.

If on the other hand, all your data is already cardinal, and you have a separate transformation matrix, you can apply it with 3dWarp which has an option (-fsl_matvec) for using an FSL affine transformation matrix and making it AFNI compatible.

If you still have questions after trying these things out, you can upload the data using the link on the left, and I'll try to figure it out.