Sr2FeMnO5+y, was synthesized under two different conditions, in air and in argon, both of which resulted in a cubic, Pm (3) over barm, structure with no long-range ordering of oxygen vacancies. The unit cell constants were found to be a(0) = 3.89328(1) angstrom for argon (y = 0.0) and a(0) = 3.83075(3) angstrom for air (y = 0.5). In contrast, Ca2FeMnO5 retains long-range brownmillerite oxygen vacancy ordering for either air or argon synthesis. Remarkably, Sr2FeMnO5.0 oxidizes spontaneously in air at room temperature. A neutron pair distribution function (NPDF) study of Sr2FeMnO5.0(Ar) showed evidence for local, brownmillerite-like ordering of oxygen vacancies for short distances up to 5 angstrom. Mossbauer spectroscopy results indicate more than one Fe site for Sr2FeMnO5+y(Ar and air), consistent with the noncubic local structure found by NPDF analysis. The isomer shifts and quadrupole splittings in both air- and argon-synthesized materials are consistent with the 3+ oxidation state for Fe in sites with coordination number four or five. This is confirmed by an L-edge XANES study. Mn is almost entirely in the 3+ state for Sr2FeMnO5.0(Ar), whereas Mn4+ is predominantly present for Sr2FeMnO5.5(air). Magnetic susceptibility data show zero-field-cooled/field-cooled (ZFC/FC) divergences near SO K for the Ar sample and 25 K for the air sample, whereas Ca2FeMnO5 is long-range G-type antiferromagnetically ordered at 407(2) K. Hyperfine magnetic splitting, observed in temperature-dependent Mossbauer measurements, indicates short-range magnetic correlations that persist up to 150 K for Sr2FeMnO5.0(Ar) and 100 K for Sr2FeMnO5.5(air), well above the ZFC/FC divergence temperatures. Neutron diffraction data confirm the absence of long-range magnetic ordering at room temperature and 4K for Sr2FeMnO5.0(Ar) but indicate the presence of domains with short-range G-type order at 4 K with an average dimension of similar to 50 angstrom (y = 0); thus, this material is actually a superparamagnet rather than a true spin glass. In sharp contrast, corresponding data for Sr2FeMnO5.5(air) show mainly a very weak magnetic Bragg peak, indicating that similar to 4% of the sample has G-type antiferromagnetic ordering at 4 K.