We present a combined experimental and theoretical study on strong-field ionization of a three-dimensionally-oriented asymmetric top molecule, benzonitrile (C7H5N), by circularly polarized, nonresonant femtosecond laser pulses. Prior to the interaction with the strong field, the molecules are quantum-state selected using a deflector and three-dimensionally (3D) aligned and oriented adiabatically using an elliptically polarized laser pulse in combination with a static electric field. A characteristic splitting in the molecular frame photoelectron momentum distribution reveals the position of the nodal planes of the molecular orbitals from which ionization occurs. The experimental results are supported by a theoretical tunneling model that includes and quantifies the splitting in the momentum distribution. The focus of the present article is to understand strong-field ionization from 3D-oriented asymmetric top molecules, in particular the suppression of electron emission in nodal planes of molecular orbitals. In the preceding article [Dimitrovski et al., Phys. Rev. A 83, 023405 (2011)] the focus is to understand the strong-field ionization of one-dimensionally-oriented polar molecules, in particular asymmetries in the emission direction of the photoelectrons.