Using theoretical formulations to describe the general response of an orthogonally woven glass-epoxy composite subjected to off-axis tension loading, a simple experimental methodology incorporating stereovision and 3D digital image correlation (3D-DIC) into several optimization procedures is described that provides a direct approach for quantitatively determining all of the elastic properties. During each off-axis tensile loading experiment, axial strains are determined using both mechanical extensometry and 3D-DIC, with the 3D-DIC measurements also used to extract both the in-plane transverse normal strain and the shear strain fields. The effectiveness of various optimization procedures are then evaluated and compared by performing a series of off-axis tensile loading experiments to determine the material engineering constants, including E1, E2, G12, and v12 for the nominally transversely isotropic material. Results indicate excellent agreement between the extensometer measurements and the average axial strain obtained by 3D-DIC. Furthermore, direct comparison of the proposed optimization methods indicates that each method is robust and effective, especially when employing 3D-DIC to extract additional information to complete the elastic property characterization procedure.