We study asymmetric reflection and nonreciprocal transmission in a non-Hermitian optomechanical system, which contains a ring optomechanical resonator, a tapered fiber waveguide, and a nanotip. Benefiting from the combination of coherent and dissipative coupling, phase-controlled nonreciprocal optical coupling can be generated, leading to asymmetric reflection. Meanwhile, the equivalent synthetic magnetism induced by a directionally fixed strong pump can break Lorentz reciprocity, thereby enabling nonreciprocal transmission. When dissipative and coherent couplings are balanced and the phase is matched, exceptional points (EPs) emerge where a contrast ratio of up to $100\%$ can be realized. Remarkably, these direction-dependent behaviors can be dynamically modulated through tuning the optical coupling, and can even be completely reversed by controlling the phase to transform odd EPs into even EPs. Furthermore, the system allows the signal from a specific input port to be transmitted to the two output ports, thereby realizing effective quantum routing. Our study not only reveals the critical role of EPs in the direction-dependent behavior, but also provides an efficient strategy for developing high-performance integrated nonreciprocal devices.