By coupling together anisotropic electromagnetic and elastodynamic properties, piezoelectric composite materials have much to offer as multifunctional metamaterials. The linear strong-property-fluctuation theory (SPFT) may be implemented to estimate the effective constitutive parameters of certain piezoelectric composite materials in the long-wavelength regime. A key feature of the SPFT homogenization approach - which distinguishes it from other more conventional homogenization approaches-is the accommodation of higher-order characterizations of the distributional statistics of the component materials. We used the SPFT to investigate homogenized composite materials (HCMs) which arose from component materials that were generally orthorhombic mm2 piezoelectric materials and were randomly distributed as oriented ellipsoidal particles. Based on our representative numerical calculations, we concluded that: (i) the lowest-order SPFT estimates are qualitatively similar to those provided by the corresponding Mori-Tanaka homogenization formalism, but certain differences between the two estimates become more pronounced as the component particles become more eccentric in shape; and (ii) the second-order SPFT estimate provides a significant correction to the lowest-order estimate, which reflects dissipative losses due to scattering.'.