We analyze the dynamic moduli of nematic polymers in a parallel plate oscillatory shear experiment from a Doi-Marrucci-Greco orientation tensor formulation, paying special attention to the inherent connection between rheological properties and wall anchoring conditions. We assume standard experimental procedures in which the plates have been rubbed to achieve strong nematic anchoring parallel to the rubbing direction. We derive the heterogeneous, harmonic response of the nematic liquid in the weak oscillatory shear regime of linear viscoelasticity. The response function is parameterized by the orientational anchoring condition and, in particular, by the angle of rotation between the rubbing direction and the flow direction. From this analysis, we read off the frequency-dependent storage and loss moduli. The dominant effect is in the storage modulus where for high frequencies rubbing aligned with the vorticity axis can cause G (') to be two to three orders of magnitude larger than rubbing in the flow direction. This anchoring dependency shows the significance of the order parameter fluctuations of tensor-based models: the Leslie-Ericksen theory predicts zero storage modulus for vorticity-aligned anchoring. For low frequencies, this effect is reversed with flow-aligned anchoring maximizing G (') in a manner similar to the Leslie-Ericksen theory although we predict a nonzero modulus for vorticity-aligned anchoring.