In van der Waals (vdW) materials, weak interlayer coupling generally suppresses vertical dispersion, reinforcing the conventional paradigm that in-plane transport dominates over cross-layer channels. Here, using first-principles calculations and magnetic symmetry analyses, we uncover a giant, symmetry-unlocked cross-layer anomalous Hall conductivity (AHC) in the vdW altermagnet V2Te2O. In the magnetic ground state with Neel vector N//z, horizontal mirror symmetry protects a spin-polarized nodal chain near the Fermi level and strictly enforces zero anomalous Hall response. Tilting the Neel vector explicitly breaks this mirror protection, allowing spin-orbit coupling to gap the nodal chain and activate a sharp cross-layer Hall response. When the Neel vector is rotated into the in-plane configuration (N//x), cross-layer orbital hybridization generates intensive Berry curvature hotspots, boosting the cross-layer component of AHC σ_yz to approximately 255 S/cm, which exceeds in-plane component σ_xy by nearly two orders of magnitude. Furthermore, varying the azimuthal angle systematically redistributes the anomalous Hall response, enabling full directional control of transverse transport. Our findings demonstrate a highly sensitive cross-layer anomalous Hall switch activated by low-barrier spin canting, offering promising avenues for directional tensor selection and low-power multi-axial vdW spintronics.