The crystal structures of the series of ordered double perovskites Ba2-xSrxYIrO6 (0 <= x <= 2) were refined using a combination of high-resolution synchrotron X-ray and high-intensity neutron diffraction data. The materials displayed a sequence of structures Fm (3) over barm(a(0)a(0)a(0)) (x=0.6) -> I4/m(a(0)a(0)c(-)) (x=1.0) -> I2/m(a(-)a(-)c(0)) (x=1.4) -> P2(1)/n(a(-)a(-)c(+)) associated with increased tilting of the corner-sharing octahedra induced by increasing amount of the smaller Sr cation present. A similar sequence of transitions was induced by heating selected samples. Magnetic susceptibility measurements between 2 and 300 K showed no evidence for long-range magnetic ordering, an observation that was supported by neutron diffraction measurements, and rather strong spin-orbit coupling results in a J(eff) = 0 ground state.