  Odd viscous liquids are endowed with an intrinsic mechanism that tends to
restore a displaced particle back to its original position. Since the odd
viscous stress does not dissipate energy, inertial oscillations and
inertial-like waves can become prominent in such a liquid. In this article we
show that an odd viscous liquid in \emph{three} dimensions gives rise to such
axially symmetric waves and also to plane-polarized waves. We tacitly assume
that an anisotropy axis giving rise to odd viscous effects has already been
established and proceed to investigate the effects of odd viscosity on fluid
flow behavior. Numerical simulations of the full Navier-Stokes equations show
the existence of inertial-like waves downstream a body that moves slowly along
the axis of an odd viscous liquid-filled cylinder. The wavelength of the
numerically-determined oscillations agrees well with the developed theoretical
framework. When odd viscosity is the dominant effect in steady motions, a
modified Taylor-Proudman theorem leads to the existence of Taylor columns
inside such a liquid. Formation of the Taylor column can be understood as a
consequence of helicity segregation and energy transfer along the cylinder axis
at group velocity, by the accompanying inertial waves, whenever the reflection
symmetry of the system is lost. A number of Taylor column characteristics known
from rigidly-rotating liquids, are recovered here for a \emph{non-rotating} odd
viscous liquid. These include counter-rotating swirling liquid flow above and
below a body moving slowly along the anisotropy axis.
