Terahertz wave (THz-wave) parametric oscillations with a noncollinear phase-matching scheme at polariton resonance using a MgO:LiNbO3 crystal with a surface-emitted configuration are investigated. We investigate frequency tuning characteristics of a THz-wave via varying the wavelength of the pump wave and phase-matching angle. The effective parametric gain length under the noncollinear phase-matching condition is calculated. Parametric gain and absorption characteristics of a THz-wave in the vicinity of polariton resonances are analyzed.