We present a detailed room-temperature x-ray powder diffraction study on La2-xSrxNiO4+delta with 0less than or equal toxless than or equal to0.12 and 0less than or equal todeltaless than or equal to0.13. For x=0.02, 0.04, and 0.06 the oxygen content phase diagrams of the Sr-doped samples show a similar sequence of pure phases and miscibility gaps as for pure La2NiO4+delta. We find a weak Sr-doping dependence of the delta range for the pure low-temperature orthorhombic (LTO), low-temperature tetragonal, and high-temperature tetragonal (HTT) phases, but overall, the delta ranges of the different phases do not vary strongly for xless than or equal to0.06. Drastic changes are observed for x=0.08 and 0.12, where miscibility gaps successively disappear. For x=0.12 all oxygen-doped samples are in the HTT phase. The mechanism responsible for the suppression of the phase separation seems to involves multiple factors, including the Coulomb interaction between Sr impurities and interstitial oxygens as well as the reduction of the NiO6 octahedral tilt angle. The doping dependence of the lattice parameters shows clear differences for pure Sr and pure O doping. With the exception of the LTO phase, the in-plane lattice parameters explicitly depend on the type of dopant, rather than the net hole content p=x+2delta. In contrast, the orthorhombic strain in the LTO phase as well as the c-axis length appears to depend only on p, however, in the case of the c-axis length this "universal" behavior turns out to be coincidental. Our results also show that the chemical pressure of La-site dopants is highly anisotropic, whereas that of O interstitials appears to be more isotropic. In general, this study reveals that for an investigation of the intrinsic properties of La2-xSrxNiO4 with xless than or similar to0.12, samples have to be annealed carefully to achieve delta=0, since already an excess oxygen content as small as delta=0.01 leads to phase separation.