We present a comprehensive study of the magnetic properties of Sr3-xYx(Fe1.25Ni0.75)O-7(-delta )(0 <= x <= 0.75). Experimentally, the magnetic properties are investigated using superconducting quantum interference device (SQUID) magnetometry and neutron powder diffraction (NPD). This is complemented by a theoretical study based on density functional theory as well as the Heisenberg exchange parameters. Experimental results show an increase in the Ned temperature (T-N) with an increase of Y concentrations and O occupancy. The NPD data reveal that all samples are antiferromagnetically ordered at low temperatures, which has been confirmed by our theoretical simulations for the selected samples. Our first-principles calculations suggest that the three-dimensional magnetic order is stabilized due to finite interlayer exchange couplings. The latter give rise to finite interlayer spin-spin correlations, which disappear above T-N.