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This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.-- et al. ; The intimate relationship between stoichiometry and physicochemical properties in transition-metal oxides makes them appealing as tunable materials. These features become exacerbated when dealing with nanostructures. However, due to the complexity of nanoscale materials, establishing a distinct relationship between structure-morphology and functionalities is often complicated. In this regard, in the FexO/Fe3O4 system a largely unexplained broad dispersion of magnetic properties has been observed. Here we show, thanks to a comprehensive multi-technique approach, a clear correlation between the magneto-structural properties in large (45 nm) and small (9 nm) FexO/Fe3O4 core/shell nanoparticles that can explain the spread of magnetic behaviors. The results reveal that while the FexO core in the large nanoparticles is antiferromagnetic and has bulk-like stoichiometry and unit-cell parameters, the FexO core in the small particles is highly non-stoichiometric and strained, displaying no significant antiferromagnetism. These results highlight the importance of ample characterization to fully understand the properties of nanostructured metal oxides. ; This work was supported by the 2014-SGR-1015 and 2009-SGR-35 projects of the Generalitat de Catalunya, by the MAT2010-20616-C02, MAT2011-27380-C02-01, MAT2010-16407, MAT2013-48628-R and CSD2009-00013 projects of the Spanish Ministerio de Economía y Competitividad (MINECO), the ONDA and COEFNANO projects (no. FP7-PEOPLE-2009-IRSES-247518 and no. FP7-PEOPLE-2012-IRSES-318901) of the European Union, the Russian grants RFBR 13-02-00121, 13-02-12429 and RG 14.B25.31.0025, the Brazilian grants CNPq-304368/2010-5 and FAPEMIG-PPM 00319-11, the Argentine grants PIP 1333 (CONICET) and SECTyP 06/C404 (Univ. Nac. de Cuyo) and the Swedish Research Council (VR). Research at NCSR "D" was supported by the HSF-EU program ARISTEIA, grant COMANA/22. GSA was partially supported by the Knut and Alice Wallenberg Foundation (Project: 3DEM-NATUR). I.V.G. thanks the Generalitat de Catalunya for his sabbatical fellowship (2010 PIV 00096). M.D.B. was partially supported by an ICREA Academia award. M.E. acknowledges the Spanish Ministry of Science and Innovation through the Juan de la Cierva Program. A. G. Roca would like to thank Generalitat de Catalunya for financial support under the Beatriu de Pinós fellowship program (2011 BP_B 00209). ICN2 acknowledges support from the Severo Ochoa Program (MINECO, grant SEV-2013-0295). ; Peer Reviewed