  There has been considerable interest in magnetoacoustic waves in static,
straight, field-aligned, one-dimensional equilibria where the exteriors of a
magnetic slab are different between the two sides. We focus on trapped,
transverse fundamental, oblique quasi-kink modes in pressureless setups where
the density varies continuously from a uniform interior (with density
$\rho_{\rm i}$) to a uniform exterior on either side (with density $\rho_{\rm
L}$ or $\rho_{\rm R}$), assuming $\rho_{\rm L}\le\rho_{\rm R}\le\rho_{\rm i}$.
The continuous structuring and oblique propagation make our study new relative
to pertinent studies, and lead to wave damping via the Alfv$\acute{\rm e}$n
resonance. We compute resonantly damped quasi-kink modes as resistive
eigenmodes, and isolate the effects of system asymmetry by varying $\rho_{\rm
i}/\rho_{\rm R}$ from the ``Fully Symmetric'' ($\rho_{\rm i}/\rho_{\rm
R}=\rho_{\rm i}/\rho_{\rm L}$) to the ``Fully Asymmetric'' limit ($\rho_{\rm
i}/\rho_{\rm R}=1$). We find that the damping rates possess a nonmonotonic
$\rho_{\rm i}/\rho_{\rm R}$-dependence as a result of the difference between
the two Alfv$\acute{\rm e}$n continua, and resonant absorption occurs only in
one continuum when $\rho_{\rm i}/\rho_{\rm R}$ is below some threshold. We also
find that the system asymmetry results in two qualitatively different regimes
for the phase and group diagrams. The phase and group trajectories lie
essentially on the same side (different sides) relative to the equilibrium
magnetic field when the configuration is not far from a ``Fully Asymmetric''
(``Fully Symmetric'') one. Our numerical results are understood by making
analytical progress in the thin-boundary limit, and discussed for imaging
observations of axial standing modes and impulsively excited wavetrains.
