The oblique interaction of interfacial solitary waves is studied in an inviscid two-layer deep-fluid system. We first derive the interaction equations correct up to the second order in an amplitude parameter by employing a systematic perturbation method. We then solve the equations exactly to investigate the properties of the interaction process of two solitary waves. In the first order, the solution is represented simply by a superposition of two algebraic solitary waves, each being the solution of the Benjamin-Ono equation. In the second order, the effect of the interaction appears as a product of two solitary waves, in addition to the corrections to the the wave profile and phase shift. We find that in the leading order of the amplitude expansion, the phase shift of each solitary wave does not depend on the amplitude and in the next order it is proportional to the amplitude. The head-on collision of two solitary waves is also considered as a special case. It is worth remarking that there exist a few cases of experimental evidence, as well as a numerical calculation, supporting the analytical prediction of the backward phase shift exhibited in the head-on collision.