We study odd-even high-harmonic generation (HHG) from oriented asymmetric molecules with different symmetries in strong laser fields. A model based on strong-field approximations is used which allows us to resolve the contributions of different emission routes to odd-even HHG. The comparison between the HHG yields of all routes versus one certain route demonstrates that the routes in which the electron ionizes from the gerade component of the asymmetric orbital contribute mainly to odd-even HHG. We show that the potential mechanism is associated with effects of intramolecular interference in tunneling ionization as the bound electron passes through the barrier formed by the laser field and the asymmetric Coulomb potential. The influences of different emission routes on asymmetric orbital imagining with odd-even HHG are also addressed.