Realizing precise control over multiquanta emission is crucial for quantum information processing, especially when integrated with advanced techniques of manipulating quantum states. Here, by spinning the resonator to induce the Sagnac effect, we can obtain nonreciprocal photon-phonon and photon-magnon super-Rabi oscillations under conditions of optically driving resonance transitions. Opening dissipative channels for such super-Rabi oscillations enables the realization of directional bundle emissions of entangled photon-phonon pairs and photon-magnon pairs by transferring the pure multiquanta state to a bundled multiquanta outside of the system. This nonreciprocal emission is a flexible switch that can be controlled with precision, and simultaneous emissions of different entangled pairs (such as photon-phonon or photon-magnon pairs) can even emerge but in opposite directions by driving the resonator from different directions. This ability to flexibly manipulate the system allows us to achieve directional entangled multiquanta emitters, and has also potential applications for building hybrid quantum networks and on-chip quantum communications.