Since oxide materials like Sr₂FeMoO₆ are usually applied as thin films, we studied the effect of biaxial strain, resulting from the substrate, on the electronic and magnetic properties and, in particular, on the formation energy of point defects. From our first-principles calculations, we determined that the probability of forming point defects, like vacancies or substitutions, in Sr₂FeMoO₆ could be adjusted by choosing a proper substrate. For example, the amount of antisite disorder can be reduced with compressive strain in order to obtain purer Sr₂FeMoO₆ as needed for spintronic applications, while the formation of oxygen vacancies is more likely for tensile strain,which improves the functionality of Sr₂FeMoO₆ as a basis material of solid oxide fuel cells. In addition, we were also able to include the oxygen partial pressure in our study by using its thermodynamic connection with the chemical potential. Strontium vacancies become, for example, more likely than oxygen vacancies at a pressure of 1 bar. Hence, this degree of freedom might offer in general another potential method for defect engineering in oxides aside from, e.g., experimental growth conditions like temperature or gas pressure.