A systematic study of epitaxially grown Sr2FeMoO6 thin films on SrTiO3, (LaAlO3)(0.3) (Sr2AlTaO6)(0.7), SrLaAlO4 and MgO single crystal substrates were made. Transmission electron microscopy investigations showed sharp substrate/films interfaces and increased defect concentration with increased lattice mismatch, indicating defect formation such as dislocations, low angle grain boundaries and stacking faults as a strain relaxation mechanism. Large enough compressive mismatch cause the over-relaxation of the lattice parameters through reorganization or interface defects, which was observed as a tensile strain in films with compressive mismatch larger than -1.05%. All the films with compressive mismatch were phase pure and epitaxially textured while signatures of SrMoO4 parasitic particle was found only in the film grown on MgO. No correlation between the antisite disorder and other structural defects or magnetic properties were found. Instead, the saturation magnetization, Curie temperature, magnetic domain rotation etc are higly dependent on the lattice mismatch induced defects, which outshines the possible correlation with B-site ordering.