In a recent discovery (Wen et al 2022 Phys. Rev. Lett. 129 045001), streaming waves were found in multipactor-induced plasma discharges. However, due to the limitations of a 1D simulation setup, these waves displayed only transverse dynamics. In this letter, an extended 2D particle-in-cell/Monte Carlo model is used to simulate multipactor-induced plasma discharge above a dielectric surface. The results reveal that the streaming waves are not solely transverse but oblique, featuring both transverse and longitudinal components of the wave vector. Furthermore, it is identified that the sheath-accelerated field-emission electrons, rather than the previously reported secondary emission electrons, predominantly cause the excitation of streaming waves. The simulated wave spectrum achieves an excellent agreement with the theoretical dispersion relation. The identification of oblique streaming waves provides new insights into multipactor physics and is anticipated to inspire novel mitigation strategies for multipactor-induced breakdown processes.