The kagome metals AV₃Sb₅ (A = K, Rb, Cs) provide a unique platform to investigate the physics of interacting electrons, a central challenge in condensed matter physics. A key obstacle in unraveling their correlated behavior is to determine which structural and electronic degrees of freedom are involved and how they couple. Here, we address this important issue with a novel approach, namely by exploring the strain dependence of electronic superlattices (SL) in CsV₃Sb₅. Using high-resolution x-ray diffraction, we track the detwinning of the 2 × 2 × 4 electronic crystal and uncover a gigantic strain response of its domains. We further show that the detwinned 2 × 2 × 4 phase exhibits an intrinsic double-q modulation and strong mode coupling. Density functional theory reveals that the structural 2 × 2 × 4 modulation couples strongly to the V 3d-orbitals, naturally explaining its pronounced strain response. In contrast, the 2 × 2 × 2 phase at lower temperatures remains essentially unaffected by small uniaxial strain. This dichotomy points to fundamental differences in the symmetry breaking and stabilization mechanisms of the two electronic orders. More specifically, our results provide evidence for the active role of orbital degrees of freedom, which can realize distinct, complex ordering patterns driven by competing interactions.