Relative integrated cross sections are measured for rotationally inelastic scattering of NO((2)Pi(1/2)), hexapole selected in the upper Lambda-doublet level of the ground rotational state (j=0.5), in collisions with He at a nominal energy of 514 cm-1. Application of a static electric field E in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the state-selected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laser-induced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, SA=(sigma(vup arrowdown arrowE)-sigma(vup arrowup arrowE))/(sigma(vup arrowdown arrowE)+sigma(vup arrowup arrowE)), which is equal to within a factor of (-1) to the molecular steric effect, Si-->f=(sigma(He-->NO)-sigma(He-->ON))/(sigma(He-->NO)+sigma(He-->ON)). The dependence of the integral inelastic cross section on the incoming Lambda-doublet component is also observed as a function of the final rotational (j(')), spin-orbit (Omega'), and Lambda-doublet (epsilon') state. The measured steric asymmetries are significantly larger than previously observed for NO-Ar scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NO-He collisions is not very sensitive to the value of Omega'. However, the Lambda-doublet propensities are very different for [Omega=0.5(F-1)-->Omega(')=1.5(F-2)] and [Omega=0.5(F-1)-->Omega(')=0.5(F-1)] transitions. Spin-orbit manifold conserving collisions exhibit a propensity for parity conservation at low Deltaj, but spin-orbit manifold changing collisions do not show this propensity. In conjunction with the experiments, state-to-state cross sections for scattering of oriented NO((2)Pi) molecules with He atoms are predicted from close-coupling calculations on restricted coupled-cluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R. Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electron-pair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry Si-->f of the inelastic cross sections at E-tr=514 cm(-1) is in reasonable agreement with that derived from the present experimental measurements for both spin-manifold conserving (F-1-->F-1) and spin-manifold changing (F-1-->F-2) collisions, except that the overall sign of the effect is opposite. Additionally, calculated field-free integral cross sections for collisions at E-tr=508 cm(-1) are compared to the experimental data of Joswig [J. Chem. Phys. 85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy E-tr=491 cm(-1) is compared to experimental data of Westley [J. Chem. Phys. 114, 2669 (2001)] for the spin-orbit conserving transition F-1 (j=0.5)-->F(1)f (j(')=3.5). (C) 2004 American Institute of Physics.