Engineering stoichiometry and lattice field in transition metal oxides (TMOs) is recognized as a promising approach for achieving emergent functional properties and exploring fundamental scientific questions. To overcome the constraints of rigid epitaxial TMOs, this study releases and transfers freestanding SrTiO3-δ (STO3-δ) membranes, derived using a water-dissolution method from STO3-δ/Sr3Al2O6/SrTiO3, onto flexible polyimide. In-plane mechanical strains were then applied to investigate the strain evolution-induced ferromagnetism. Continuous strain modulates interplane and intraplane exchange interactions between neighboring atoms in the ferromagnetic STO3-δ membranes, thereby influencing their ferromagnetic properties. STO3-δ initially undergoes in-plane octahedral distortion when strain is less than 1.5 %, followed by a decrease in the out-plane lattice constant. This structural variation leads to complex strain-dependent behaviors in the saturation magnetic moment (Ms) and coercive field (Hc) of STO3-δ, with Ms and Hc exhibiting a nonlinear, volcano-shaped, and step-wise correlation, respectively. Our research demonstrates that freestanding STO3-δ serves as a platform for studying local defects and their impacts on tunable magnetic properties, greatly enhancing our understanding of t2g electron engineering through modulable inter/intra plane exchange coupling with lattice field.