Following earlier theoretical predictions, intercalated compounds in the V${}_2$Se${}_2$O family, including RbV${}_2$Te${}_2$O and KV${}_2$Se${}_2$O, have been experimentally identified as $d$-wave altermagnets. This family represents the only verified class of van der Waals altermagnets to date. Their layered structure and crystal-symmetry $𝒞$-paired spin-momentum locking (CSML) make them a promising platform for exploring unconventional spin responses in low-dimensional systems. To establish a realistic theoretical foundation for understanding these materials, we construct a symmetry-constrained tight-binding model with parameters fitted to first-principles calculations for six representative members of this family. The model reproduces the low-energy band structures and CSML both with and without spin-orbit coupling, enabling calculations of transport responses such as noncollinear spin currents. We further incorporate strain-dependent parameters to describe strain-tunable responses such as the piezo-Hall effect. This model provides a framework for studying electronic structure and spin transport, as well as the interplay among spin, valley, and layer degrees of freedom. More broadly, it provides a starting point for future investigations of novel physics in layered altermagnets and related low-dimensional systems.