The influence of disorder and stoichiometry-breaking point defects on the structural and magnetic properties of Sr2FeMoO6 have been investigated with the help of electronic structure calculations within the spin-polarized GGA+U approach. Defining the chemical potentials of the constituent elements from constitutional defects, we calculate the energetics of the possible point defects in nonstoichiometric Sr2FeMoO6 and find transition-metal-ion antisites and oxygen vacancies to be dominant. In nonstoichiometric Sr2Fe1+xMo1-xO6 with -0.75 <= x <= 0.25, both Fe-Mo antisites (for Fe-rich samples or x > 0) and Mo-Fe antisites (for Mo-rich samples or x < 0) lead to a systematic decrease in saturation magnetization. Only Mo-Fe antisites destroy the half-metallic character of the electronic structure, since their t(2g) band crosses the Fermi level for x <= -0.125. This leads to a decrease of spin polarization from 100% for x >= -0.125 to 0 at x approximate to -0.75. Oxygen vacancies also reduce the saturation magnetization, but the half-metallic character and, hence, 100% spin polarization is retained. The optimized unit-cell lattice parameter remains within a relatively narrow range (7.96 angstrom for x = +0.25 to 8.00 angstrom for x = -0.75), despite large changes in composition. In stoichiometric Sr2FeMoO6, the saturation magnetization decreases linearly as the Fe/Mo antisite disorder increases, and the half metallicity is lost, because of the t(2g) states on both Mo-Fe and Fe-Mo. The spin polarization remains similar to 100% only for very small amounts of disorder. The calculated disorder formation energies suggest that short-range ordering is favorable in Sr2FeMoO6. The calculated results are in excellent quantitative agreement with experimental values, where available.