Sr2Fe3Se2O3 is a localized-moment iron oxide selenide in which two unusual coordinations for Fe2+ ions form two sublattices in a 2:1 ratio. In the paramagnetic region at room temperature, the compound adopts the crystal structure first reported for Sr2Co3S2O3, crystallizing in space group Pbam with a = 7.8121 angstrom, b = 10.2375 angstrom, c = 3.9939 angstrom, and Z = 2. The sublattice occupied by two-thirds of the iron ions (Fe2 site) is formed by a network of distorted mer-[FeSe3O3] octahedra linked via shared Se-2 edges and O vertices forming layers, which connect to other layers by shared Se vertices. As shown by magnetometry, neutron powder diffraction, and Mossbauer spectroscopy measurements, these moments undergo long-range magnetic ordering below T-N1 = 118 K, initially adopting a magnetic structure with a propagation vector (1/2 - delta, 0, 1/2) (0 <= delta <= 0.1) which is incommensurate with the nuclear structure and described in the Pbam1' (a01/2)000s magnetic superspace group, until at 92 K (T-INC) there is a first order lock-in transition to a structure in which these Fe2 moments form a magnetic structure with a propagation vector (1/2, 0, 1/2) which may be modeled using a 2a x b x 2c expansion of the nuclear cell in space group 36.178 B(a)b2(1)m (BNS notation). Below T-N2 = 52 K the remaining third of the Fe2+ moments (Fe1 site) which are in a compressed trans-[FeSe4O2] octahedral environment undergo long-range ordering, as is evident from the magnetometry, the Mossbauer spectra, and the appearance of new magnetic Bragg peaks in the neutron diffractograms. The ordering of the second set of moments on the Fe1 sites results in a slight reorientation of the majority moments on the Fe2 sites. The magnetic structure at 1.5 K is described by a 2a x 2b x 2c expansion of the nuclear cell in space group 9.40 I(a)b (BNS notation).