The integral steric asymmetry for the inelastic scattering of NO(X) by a variety of collision partners was recorded using a crossed molecular beam apparatus. The initial state of the NO(X, v = 0, j = 1/2, Ω=1/2, ϵ=-1,f) molecule was selected using a hexapole electric field, before the NO bond axis was oriented in a static electric field, allowing probing of the scattering of the collision partner at either the N- or O-end of the molecule. Scattered NO molecules were state selectively probed using (1 + 1') resonantly enhanced multiphoton ionisation, coupled with velocity-map ion imaging. Experimental integral steric asymmetries are presented for NO(X) + Ar, for both spin-orbit manifolds, and Kr, for the spin-orbit conserving manifold. The integral steric asymmetry for spin-orbit conserving and changing transitions of the NO(X) + O2 system is also presented. Close-coupled quantum mechanical scattering calculations employing well-tested ab initio potential energy surfaces were able to reproduce the steric asymmetry observed for the NO-rare gas systems. Quantum mechanical scattering and quasi-classical trajectory calculations were further used to help interpret the integral steric asymmetry for NO + O2. Whilst the main features of the integral steric asymmetry of NO with the rare gases are also observed for the O2 collision partner, some subtle differences provide insight into the form of the underlying potentials for the more complex system.