Single charge transfer in low-energy Na++87Rb(5s,5p) collisions is investigated using magneto-optically trapped Rb atoms and high-resolution recoil-ion momentum spectroscopy. The three-dimensional reconstruction of the recoil-ion momentum provides accurate relative cross-sections for the active channels and the projectile scattering angle distributions. Thanks to the high experimental resolution, scattering structures such as diffractionlike oscillations in angular distributions are clearly observed. The measurements are compared with molecular close-coupling calculations and an excellent agreement is found. To go further in the test of the theory, the target is prepared in an oriented state. It is the first time that such collision experiments with oriented target is performed with such a high resolution. The right-left asymmetry expected for the scattering angle distribution is evidenced. The agreement between MOCC calculations and experiments is very good. Simple models developped for collisons with oriented target are also discussed.