We examine the impact of the combination of a static electric field and a non-resonant linearly polarized laser field on an asymmetric top molecule. Within the rigid rotor approximation, we analyze the symmetries of the Hamiltonian for all possible field configurations. For each irreducible representation, the Schrödinger equation is solved by a basis set expansion in terms of a linear combination of symmetric top eigenfunctions respecting the corresponding symmetries, which allows us to distinguish avoided crossings from genuine ones. Using the fluorobenzene and pyridazine molecules as prototypes, the rotational spectra and properties are analyzed for experimentally accessible static field strengths and laser intensities. Results for energy shifts, orientation, alignment, and hybridization of the angular motion are presented as the field parameters are varied. We demonstrate that a proper selection of the fields gives rise to a constrained rotational motion in three Euler angles, the wave function being oriented along the electrostatic field direction, and aligned in other two angles.