We study the rheological response of monodomain ellipsoidal biaxial liquid crystal polymers (BLCP) as well as bent-core or V-shaped liquid crystal polymers (VLCP) subject to steady and time-dependent small amplitude oscillatory shear in selected regions of the model as well as flow parameter space. We adopt the two newly developed hydrodynamical kinetic theories for ellipsoidal BLCPs and VLCPs, respectively (Sircar and Wang, PRE 78:061702, 2008, J Rheol 53:819-858, 2009; Sircar et al., Comm Math Sci (in press), 2010), in which a generalized Straley's potential is used to represent the pairwise mean-field interaction of the mesoscopic system in biaxial phases. Transient shear stresses and normal stress differences corresponding to steady and small amplitude oscillatory shear are investigated; their variations with respect to the strength of the intermolecular potential, types of biaxial interaction, and changes in the aspect ratios for ellipsoidal BLCPs and the bent angle for VLCPs are explored.