In this paper we use the Schwinger multichannel method (SMC) to calculate several types of cross sections related to the elastic electron scattering by NO. We show through the NO system that the elastic scattering of an electron by an open shell molecule is a much richer process than the corresponding scattering by closed shell targets. We present cross sections for unpolarized electron scattering by (oriented and nonoriented) molecules, spin-flip cross sections (in the form of polarization fractions), and zero-energy electronic excitation cross sections (due to orbital degeneracy of the NO ground state). Our results agree well with published experimental values for elastic unpolarized data as well as recent polarized electron-NO scattering. We also present a detailed study of the dependence of the polarization fraction on molecular orientation. Our results also show a shape resonance which is also seen experimentally around 18 eV, and we suggest its symmetry.