  The insulating iron compounds Eu$_2$SrFe$_2$O$_6$ and Sr$_3$Fe$_2$O$_4$Cl$_2$
have high-temperature antiferromagnetic (AF) order despite their different
layered structures. Here we carry out density functional calculations and Monte
Carlo simulations to study their electronic structures and magnetic properties
aided with analyses of the crystal field, magnetic anisotropy, and
superexchange. We find that both compounds are Mott insulators and in the
high-spin (HS) Fe$^{2+}$ state ($S$ = 2) accompanied by the weakened crystal
field. Although they have different local coordination and crystal fields, the
Fe$^{2+}$ ions have the same level sequence and ground-state configuration
$(3z^2-r^2)^2(xz,yz)^2(xy)^1(x^2-y^2)^1$. Then, the multiorbital superexchange
produces strong AF couplings, and the $(3z^2-r^2)/(xz,yz)$ mixing via the
spin-orbit coupling (SOC) yields a small in-plane orbital moment and
anisotropy. Indeed, by tracing a set of different spin-orbital states, our
density functional calculations confirm the strong AF couplings and the easy
planar magnetization for both compounds. Moreover, using the derived magnetic
parameters, our Monte Carlo simulations give the N\'eel temperature $T_{\rm N}$
= 420 K (372 K) for the former (the latter), which well reproduce the
experimental results. Therefore, the present study provides a unified picture
for Eu$_2$SrFe$_2$O$_6$ and Sr$_3$Fe$_2$O$_4$Cl$_2$ concerning their electronic
and magnetic properties.
