  We present a systematic study on the structural properties of odd-$Z$
superheavy nuclei with proton numbers $Z=117, 119$, and neutron numbers $N$
increasing from $N=170$ to the neutron dripline within the framework of axially
deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). The
results are compared with those of even-even superheavy nuclei with proton
numbers $Z=118$ and $120$. We analyze various bulk properties of their ground
states, including binding energies, quadrupole deformations, root-mean-square
radii, nucleon separation energies, and $\alpha$-decay energies. The
coexistence of competing prolate and oblate or spherical shapes leads to abrupt
changes in both quadrupole deformations and charge radii as functions of
neutron numbers. Compared to even-even nuclei, the odd-mass ones exhibit a more
complicated transition picture, in which the quantum numbers of $K^\pi$ of the
lowest-energy configuration may change with deformation. This may result in the
change of angular momentum in the ground-state to ground-state $\alpha$-decay
and thus quench the decay rate in odd-mass nuclei. Moreover, our results
demonstrate a pronounced proton shell gap at $Z=120$, instead of $Z=114$, which
is consistent with the predictions of most covariant density functional
theories. Moreover, large neutron shell gaps are found at $N=172$ and $N=258$
in the four isotopic chains, as well as at $N=184$ in the light two isotopic
chains with $Z=117$ and $Z=118$, attributed to the nearly-degenerate $3d$ and
$4p$ spin-orbit doublet states due to the presence of bubble structure.
