A gyrostat in central Newtonian gravitational and dipolar magnetic fields is considered. It moves along a weakly elliptical Keplerian orbit in a magnetic equatorial plane. The gyrostat possesses electrostatic charge and intrinsic magnetic moment. The attitude motion under the action of Lorentz and magnetic torques is studied. It is shown that the system of differential equations of gyrostat attitude motion is reversible with three fixed sets in the case of a circular orbit. Symmetrical periodic motions of oscillatory type are analyzed. Bifurcation in a family of gyrostat symmetrical oscillations and generation of two isolated symmetrical oscillations are revealed in transition from a circular orbit to an elliptical one.