Connecting earthquake nucleation in basement rock to fluid injection in basal, sedimentary reservoirs, depends heavily on choices related to the poroelastic properties of the fluid-rock system, thermo-chemical effects notwithstanding. Direct constraints on these parameters outside of laboratory settings are rare, and it is commonly assumed that the rock layers are isotropic. With the Arbuckle wastewater disposal reservoir in Osage County, Oklahoma, high-frequency formation pressure changes and collocated broadband ground velocities measured during the passing of large teleseismic waves show a poroelastic response of the reservoir that is both azimuthally variable and anisotropic; this includes evidence of static shifts in pressure that presumably relate to changes in local permeability. The azimuthal dependence in both the static response and shear coupling appears related to tectonic stress and strain indicators such as the orientations of the maximum horizontal stress and faults and fractures. Using dynamic strains from a nearby borehole strainmeter, we show that the ratio of shear to volumetric strain coupling is $ \sim 0.41 $ which implies a mean Skempton's coefficient of $ A = 0.24 $ over the plausible range of the undrained Poisson's ratio. Since these observations are made at relatively low confining pressure and differential stress, we suggest that the hydraulically conductive fracture network is a primary control on the coupling between pore pressure diffusion and elastic stresses in response to natural or anthropogenic sources.