What Are "X-Shaped" Radio Sources Telling Us? II. Properties of a Sample of 87

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.