  In an earlier paper we presented Jansky Very Large Array multi-frequency,
multi-array continuum imaging of a unique sample of low axial-ratio radio
galaxies. In this paper, the second in the series, we examine the images to
know the phenomenology of how the off-axis emission relates to the main radio
source. Inversion symmetric offset emission appears to be bimodal and to
originate from one of two strategic locations: outer ends of radio lobes
(Outer-deviation) or from inner ends (Inner-deviation). The latter sources are
almost always associated with edge-brightened sources. With S- and Z-shaped
sources being a subset of Outer-deviation sources this class lends itself
naturally to explanations involving black hole axis precession. Our data allow
us to present a plausible model for the more enigmatic Inner-deviation sources
with impressive wings; as for outer-deviation sources these too require black
hole axis shifts although also requiring plasma backflows into relic channels.
Evolution in morphology over time relates the variety in structures in
inner-deviation sources including XRGs. With features such as
non-collinearities, central inner-S "spine", corresponding lobe emission peaks,
double and protruding hotspots not uncommon, black hole axis precession,
drifts, or flips could be active in significant fraction of radio sources with
prominent off-axis emission. At least 4\% of radio galaxies appear to undergo
black hole axis rotation. Quasars offer a key signature to recognize rotating
axes. With rich haul of sources that have likely undergone axis rotation our
work shows the usefulness of low axial-ratio sources to pursue searches for
binary supermassive black holes.
