Double perovskite ceramics Sr2FeMoO6–δ having different amount of antisite disordering and oxygen content are prepared by the solid-phase reaction method using SrFeO2.52(3) and SrMoO4 initial reagents. X-ray and neutron diffraction techniques are used to estimate a modification in the structural parameters as a function of oxygen content and B–site cationic ordering. Reduction of oxygen content leads to an increase in the unit cell volume, which is mainly associated with an elongation of c –parameter of the tetragonal unit cell and relative expansion of the chemical bonds between Mo/Fe ions and apical oxygen ions. Superstructural ordering observed for the compounds causes a decrease in the unit cell volume, which is accompanied by a reduction in the length of the Mo/Fe – O bonds, located in the basal plane of oxygen octahedra. This modification of the unit cell parameters notably affects a character of the exchange interactions formed between B–site ions thus allowing to control magnetic and transport properties of Sr2FeMoO6–δ ceramics. It is found that comprehensive approach allows a consistent understanding of much debated structural/magnetic behaviors of double perovskite Sr2FeMoO6–δ systems, opening a venue for designing reliable devices based on the half-metallic double perovskite materials.