We report the experimental observation of oscillations in the critical current Ic of SNS Josephson junctions as a function of in-plane magnetic field B|| (where S is Nb and N is Al above its critical temperature). Our theoretical calculations within the Ginzburg-Landau framework demonstrate that at sufficiently large B||, in-plane vortices enter the N layer, pin on the SN interface, and partially penetrate the S layer in the banks of the SNS junction. These interface vortices significantly affect the proximity-induced superconductivity in the normal weak link, leading to pronounced oscillations in the critical current Ic(B||). We also observe a superconducting diode effect of orbital origin that undergoes sign reversal with variations in the magnetic field.