The wave-particle cyclotron interaction is a basic process in collisionless plasmas, which results in the redistribution of the energy between plasma waves and charged particles. This paper presents an event observation in order to explore the dynamics of charged particles and plasma waves, i.e., mirror, electromagnetic ion cyclotron (EMIC), and whistler waves, in the Earth's magnetosheath. It shows that when ions have a high-speed streaming velocity parallel to the magnetic field, EMIC waves arise. We also find that the frequency distribution of nearly parallel and nearly antiparallel whistler waves depends on the parallel streaming velocity of electrons. Based on the linear kinetic theory and the fitting plasma parameters, we show that the differential flows among ion components can enhance the ion cyclotron anisotropy instability that is even stronger than the mirror instability. The differential electron flows induce an asymmetry of the growth rate of counter-propagating whistler waves in the electron cyclotron anisotropy instability. On the other hand, the low-frequency EMIC and transverse electromagnetic waves modulate the ion pitch angle distribution. Moreover, when charged particles flow across the magnetic field, both low-and high-energy electrons are deeply trapped by mirror waves. These results illustrate new features of the observed plasma waves and charged particles in the Earth's magnetosheath, which could inspire improvement of the wave models therein.