Broken symmetry and tilting effects are ubiquitous in Weyl semimetals (WSMs). Therefore, it is crucial to understand their impacts on the materials electronic and optical properties. Here, using a realistic four-band model for WSMs that incorporates both the symmetry breaking and tilting effects, we study its Landau quantization and the associated magneto-absorption spectrum. We show that the Landau levels in tilted Weyl bands can be obtained by considering a non-tilt Hamiltonian through Lorentz boost. However, broken symmetry effects can generate an additional term in the Hamiltonian, which equivalently leads to band reconstruction. Our work provides a more realistic view of the magnetic field response of WSMs that shall be taken into account in relevant future device applications.