The properties of the two-dimensional cavity polaritons subjected to the action of a strong perpendicular magnetic and electric fields, giving rise to the Landau quantization (LQ) of the 2D electrons and holes accompanied by the Rashba spin-orbit coupling, by the Zeeman splitting and by the nonparabolicity of the heavy-hole dispersion law are investigated. We use the method proposed by Rashba (1960) [1] and the obtained results are based on the exact solutions for the eigenfunctions and for the eigenvalues of the Pauli-type Hamilonians with third order chirality terms and nonparabolic dispersion law for heavy-holes and with the first order chirality terms for electrons. The selection rules of the band-to-band optical quantum transitions as well as of the quantum transitions from the ground state of the crystal to the magnetoexciton states depend essentially on the numbers n_e and n_h of the LQ levels of the (e-h) pair forming the magnetoexciton. It is shown that the Rabi frequency Ω_R of the polariton branches and the magnetoexciton oscillator strength f_osc increase with the magnetic field strength B as ^ΩR~B, and ^fosc~B. The optical gyrotropy effects may be revealed changing the sign of the photon circular polarization at a given sign of the wave vector longitudinal projection k_z or equivalently changing the sign of k_z at the same selected circular polarization.