Magnetic La <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> MnO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+δ</sub> particles of composition x = 0.36 and average size of 40 nm have been prepared from the oxidizing flux of sodium nitrite at ≈500 °C. Detailed magnetic and neutron diffraction measurements have been performed on raw nanoparticles and particles subjected to mild acid leaching. Based on these experiments and X-ray fluorescence analysis of the respective products, we conclude on the core-shell magnetic structure of the molten-salt-prepared particles, consisting of ferromagnetic (FM) ordering in the interior and A-type antiferromagnetic (AFM) ordering in the intermediate shell just below the outermost, magnetically disordered layer. The reason for such complex arrangement, unprecedented in sol-gel-prepared manganite nanoparticles of the same composition, is in a certain radial distribution of La, Sr cations, and an increased oxygen stoichiometry related to the presence of extra oxygen atoms covalently bound at the particle surface. The acid leaching, performed by consecutive treatments with ice-cold solutions of dilute nitric acid and citric acid, removes the overoxidized surface and some outer Sr-richer layers, decreasing the composition to x = 0.32. As a result, the AFM ordering is almost completely suppressed while FM ordering is preserved in the leached nanoparticles.