Mg₃Bi₂-based thermoelectric materials have attracted extensive attention due to their low-cost elemental composition and intrinsically low lattice thermal conductivity. Improving their thermoelectric performance remains a key challenge in current research. In this work, first-principles density functional theory (DFT) calculations combined with the Boltzmann transport equation (BTE) within the relaxation time approximation (RTA) are employed to systematically investigate the strain-dependent structural, phonon, electronic, and thermoelectric properties of Mg₃Bi₂ at 300 K over a wide strain range from -2.5% to +3.0%. For the electronic transport calculations, the constant relaxation time approximation (CRTA) is adopted, with the carrier relaxation time τ determined using deformation potential theory (DPT) to avoid the arbitrariness associated with empirical choices of the relaxation time. The mechanical and dynamical stability of Mg₃Bi₂ throughout the investigated strain range is confirmed by the calculated elastic constants and phonon dispersion spectra. At 300 K, the lattice thermal conductivity exhibits a pronounced asymmetric response to strain, increasing progressively from tensile to compressive strain. Compressive strain simultaneously enhances phonon group velocities and suppresses phonon scattering, resulting in a synergistic enhancement of lattice heat transport. In contrast, tensile strain produces the opposite effects and is therefore favorable for reducing the lattice thermal conductivity. Meanwhile, strain significantly modifies the electronic transport properties through changes in the electronic band structure. For n-type Mg₃Bi₂, a compressive strain of -2.5% is found to enhance the power factor by up to 54.34%, leading to a 45.48% increase in the maximum ZT compared with the unstrained state. In contrast, a tensile strain of +3.0% results in a 28.05% enhancement in the maximum ZT for p-type Mg₃Bi₂. These results reveal a clear strain-selective thermoelectric optimization strategy, in which compressive strain is favorable for n-type Mg₃Bi₂, whereas tensile strain preferentially benefits p-type Mg₃Bi₂.