The Landau quantization of the two-dimensional (2D) heavy holes, its influence on the energy spectrum of 2D magnetoexcitons, as well as their optical orientation are studied. The Hamiltonian of the heavy holes is written in twoband model taking into account the Rashba spin-orbit coupling (RSOC) with two spin projections, but with nonparabolic dispersion law and third order chirality terms. The most Landau levels, except three with m=0, 1, 2, are characterized by two quantum numbers m-3 and m for m≥3 for two spin projections correspondingly. The difference between them is determined by the third order chirality. Four lowest Landau levels (LLLs) for heavy holes were combined with two LLLs for conduction electron, which were taken the same as they were deduced by Rashba [1] in his theory of spin-orbit coupling (SOC) based on the initial parabolic dispersion law and first order chirality terms. As a result of these combinations eight 2D magnetoexciton states were formed. Their energy spectrum and the selection rules for the quantum transitions from the ground state of the crystal to exciton states were determined. On this base such optical orientation effects as spin polarization and magnetoexciton alignment are discussed. The peculiarities of the Bose-Einstein condensation of magnetoexcitons in the presence of spin-orbit interaction are discussed. IVP gratefully acknowledges the Foundation for Young Scientists of the Academy of Sciences of Moldova for the financial support (11.819.05.13F).