We present a systematic analysis of the behavior of thin films of Cd${}_3$As${}_2$ under different strain profiles and in magnetic fields. In each case, we construct effective $k\cdot p$ models by considering the reduction of symmetry and all constraints imposed by the remaining symmetries. Our analysis naturally describes both in-plane biaxial and uniaxial strain. Biaxial strain generally preserves in-plane $C_4$ rotational symmetry, but biaxial tension was experimentally shown to result in a non-centrosymmetric structure described by $4mm$ point symmetry due to Cd vacancy reordering. Uniaxial strain, on the other hand, breaks $C_4$ symmetry. For this case, we consider two scenarios: one preserving inversion, described by the $mmm$ group, and one breaking it, leading to $2mm$ symmetry. For out-of-plane magnetic fields, we show that the avoided crossing of the zeroth Landau levels observed experimentally can arise either from a strain-induced topological transition caused by band-parameter renormalization or from the simultaneous breaking of inversion and $C_4$ symmetry. We show that breaking either inversion or $C_4$ alone is insufficient to gap the crossing. Importantly, our analysis proposes a new method for differentiating between them. In the topological transition case, the critical field is continuously driven toward zero as the band parameters are renormalized, whereas in the symmetry-breaking scenario, a finite LLL anticrossing is symmetry-allowed as soon as the corresponding inversion- and $C_4$-breaking coupling is present. Furthermore, we demonstrate that a two-dimensional Dirac semimetal phase can be induced by sufficiently large in-plane magnetic fields. This phase is highly sensitive to different strain profiles, with band touchings occurring only when the field is applied perpendicular to preserved mirror planes, serving as a powerful probe of the material’s strain profile.