  We investigate the effect of strange quark degrees of freedom on the
formation of inhomogeneous chiral condensates in a three-flavor
Nambu--Jona-Lasinio model in mean-field approximation. A Ginzburg-Landau study
complemented by a stability analysis allow us to determine in a general way the
location of the critical and Lifshitz points, together with the phase boundary
where the (partially) chirally restored phase becomes unstable against
developing inhomogeneities, without resorting to specific assumptions on the
shape of the chiral condensate. We discuss the resulting phase structure and
study the influence of the bare strange-quark mass $m_s$ and the axial anomaly
on the size and location of the inhomogeneous phase compared to the first-order
transition associated with homogeneous matter. We find that, as a consequence
of the axial anomaly, critical and Lifshitz point split. For realistic
strange-quark masses the effect is however very small and becomes sizeable only
for small values of $m_s$.
