The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across to the laser propagating direction are studied in the 3/2 dimensional Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. Chirikov-like mappings which describe the recurrence relations of electrons energy and time passing through some fixed canonical variables are derived and then the criterions for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength, which for the transverse case depends only on one parameter combining the electric field strength, laser amplitude and initial condition. These maximum energies could be increased by a weak electric field. However, the maximum energy is reduced for the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly.