The magnetic and electronic modifications induced at the interfaces in (SrMnO$_{3}$)$_{n}$/(LaMnO$_{3}$)$_{2n}$ superlattices have been investigated by linear and circular magnetic dichroism in the Mn L$_{2,3}$ x-ray absorption spectra. Together with theoretical calculations, our data demonstrate that the charge redistribution across interfaces favors in-plane ferromagnetic (FM) order and $e_{g}(x^{2}-y^{2})$ orbital occupation, in agreement with the average strain. Far from interfaces, inside LaMnO$_3$, electron localization and local strain favor antiferromagnetism (AFM) and $e_{g}(3z^{2}-r^{2})$ orbital occupation. For $n=1$ the high density of interfacial planes ultimately leads to dominant FM order forcing the residual AFM phase to be in-plane too, while for $n geq 5$ the FM layers are separated by AFM regions having out-of-plane spin orientation.