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 learn 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 they also require 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 a 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 for recognizing rotating axes. With a rich haul of sources that have likely undergone axis rotation, our work shows the usefulness of low-axial ratio sources in pursuing searches for binary supermassive black holes.