Hi Brad,
1. It "rounds" to the nearest cardinal transform.
2. 3dWarp can be used to either apply the warp of a given
dataset (via -oblique2card), or apply the inverse warp of a
given dataset to a different dataset (see -oblique_parent),
e.g. apply the inverse warp of the EPI dataset to register
the anat to the EPI, so that the EPI does not need to be
interpolated.
3. See #2. The only other application is to have programs
whine at you if you change it (such as running 3dresample
on an oblique dataset, which invalidates the transform).
4. No. Warp underlay can be used either to resample it based
on the Define Datamode controls, or to apply an ACPC or TLRC
transform to a dataset that has none.
So anyway, if you want to deal with oblique data, do it via
3dWarp. The -help output has examples under "Sample usages".
Please let us know if you have any questions about that.
- rick