We report on optical excitations in the magnetically ordered phases of multiferroic Fe1.86Zn0.14Mo3O8 in the frequency range 10-130 cm-1 (0.3-3.9 THz). In the collinear easy-axis antiferromagnetic phase below TN=50 K, 11 optically active modes have been observed in finite magnetic fields, assuming that the lowest-lying mode is doubly degenerate. The large number of modes reflects either a more complex magnetic structure than in pure Fe2Mo3O8 or that spin-stretching modes become active in addition to the usual spin precessional modes. Their magnetic field dependence, for fields applied along the easy axis, reflects the irreversible magnetic-field-driven phase transition from the antiferromagnetic ground state to a ferrimagnetic state, while the number of modes remains unchanged in the covered frequency region. We determined selection rules for some of the antiferromagnetic modes by investigating all polarization configurations and identified magnetic- and electric-dipole active modes as well. In addition to these sharp resonances, a broad electric-dipole active excitation band, which is not influenced by the external magnetic field, occurs below TN with an onset at 12 cm-1. We are able to model this absorption band as a vibronic excitation related to the lowest-lying Fe2+ electronic states in a tetrahedral environment.