A self-consistent Hamiltonian model based on equations describing the coupled dynamics of whistler and lower frequency waves in inhomogeneous plasmas is built. On this basis, different aspects of whistler turbulence are studied, concerning mainly the development of modulational instabilities and the dynamics of envelope solitons in irregular plasmas. Numerical simulations based on the model show that modulational instabilities can lead to the generation of a beating of stable nonlinear whistlers propagating with a speed near the group velocity. The whistler envelope soliton is determined analytically, and its propagation in plasmas presenting random density fluctuations and weakly irregular density structures of different scales and amplitudes is studied, showing that the envelope is very weakly affected by these inhomogeneities, whereas the wavelengths and the amplitudes of the phase oscillations strongly vary. Moreover, simulations show for the first time that two whistler solitons moving with different but close velocities and colliding one with the other remain unchanged after this collision, independently of their initial amplitudes and velocities. Finally, we study the dynamics of sonic whistler envelope solitons and show that the propagation of their lower frequency perturbation is governed by a KdV-type equation.