Layered oxide intercalation compounds continue to attract interest as electrode materials for Na-ion batteries. However, many of these materials undergo complex phase transitions during cycling that influence battery performance but are still not completely understood. We have conducted a first-principles study of layered ${\mathrm{Na}}_{x}{\mathrm{CrO}}_{2}$ $(0\ensuremath{\le}x\ensuremath{\le}1)$ to assess phase stability between various Na-vacancy ordered phases in the O3 and P3 host structures. We predict that many of the low-energy phases belong to families of Na orderings that follow specific patterns. At high $x$, we identify families of vacancy row orderings in O3, which may also couple to magnetic orderings of the Cr spins. We predict similar orderings at intermediate $x$ in P3 that contain antiphase boundaries between regions of the $x=1/2$ ordering. In both cases, the average spacing between rows/boundaries is set by the overall composition. At $x=0$, we find a strong preference for charge disproportionation and migration of Cr to tetrahedral sites in the intercalation layers. We obtain generally good agreement with experimental observations and rationalize key discrepancies.