In this paper, the electron acceleration and its relativistic dynamics in an ion-channel formed due to the laser pulse propagation through the plasma and under influence of the ion channel space-charge and a heliacal wiggler as well as the oblique magnetic field have been investigated. The equations for investigation of the electron dynamics are the tree-dimension Lorentz equations. For analytical analysis of the obtained equations, a three-dimension single particle code and forth order Runge-Kutta method is used as well. The electron energy gain and the relativistic electron dynamics drastically are affected by the ion-channel potential and the helical wiggler and also the external oblique magnetic field. The results of this paper can be significant in the selection of the appropriate parameters for plasma-based accelerators design.