The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across the laser propagating direction are studied in the 3/2 dimensional (3/2D) Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of the amplitude 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 electron energy and time passing through zero canonical momentum plane are derived, and then, the criteria 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. 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.