The effective complex piezoelectric and dielectric constants of disordered heterogeneous systems of the type of statistical mixtures with the components in the form of spheroid-shaped particles equally oriented but randomly arranged in space were studied. It has been found for the first time that in such systems there appears a giant piezoelectric enhancement accompanied by a giant relaxation of piezoelectric coefficients and the dielectric permittivity. Piezoelectric and dielectric spectra differ significantly from the Debye ones and are of Davidson-Cole type. The influence of the aspect ratio of spheroids on the effects under consideration was studied. The physical mechanisms responsible for the anomalies in the behavior of piezoelectric coefficients and the dielectric permittivity were considered.