A Dirac point is a linear band crossing point originally used to describe unusual transport properties of materials like graphene. In recent years, there has been a surge of exploration of type-II Dirac/Weyl points using various engineered platforms including photonic crystals, waveguide arrays, metasurfaces, magnetized plasma and polariton micropillars, aiming toward relativistic quantum emulation and understanding of exotic topological phenomena. Such endeavors, however, have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials. We propose and demonstrate nonlinear valley Hall edge (VHE) states in laser-written anisotropic photonic lattices hosting innately the type-II Dirac points. These self-trapped VHE states, manifested as topological gap quasi-solitons that can move along a domain wall unidirectionally without changing their profiles, are independent of external magnetic fields or complex longitudinal modulations, and thus are superior in comparison with previously reported topological edge solitons. Our finding may provide a route for understanding nonlinear phenomena in systems with type-II Dirac points that violate the Lorentz invariance and may bring about possibilities for subsequent technological development in light field manipulation and photonic devices.