We have investigated the quantum magnetic oscillations of graphene subjected to the spin-orbit interaction(SOI) in the presence of crossed uniform electric and magnetic fields and scattered from impurities at finite temperatures. Landau levels are shown to be modified in an unexpected fashion by the spin-orbit interaction, the electrostatic potential and magnetic confinement; this is strikingly different from the non-relativistic 2D electron gas. Furthermore, we derive the analytical expressions of the thermodynamic quantities subject to the SOI, such as density of states, thermodynamic potential, magnetization, and magnetic susceptibility etc. At finite temperatures, the magnetization and magnetic susceptibility can both be predicted to oscillate periodically as a function of reciprocal field 1/B and shown to be modulated through the SOI and the dimensionless parameter ( = E/ F B). As approaches unity, the values of magnetization and magnetic susceptibility finally move to infinity, indicating a transformation of closed orbits into open trajectories, thereby, leading to the vanishing of magnetic oscillations. And, the magnetic susceptibility depends largely on the external fields, suggesting that graphene should be a non-linear magnetic medium. Besides, the associative effect of impurity scattering and temperature may make the standard 2D electron gas be deemed as the consequence of the relativistic type spectrum of low energy electrons and holes in graphene. Also, we comment on a possibility of using magnetic oscillations for detecting a gap that may open in the spectrum of quasiparticle excitations due to the SOI.