Using the method of periodic components, we obtain the solution to a coupled boundary value problem of electro-elasticity for piezo-active composites of random quasi-periodic structures. We consider fields of deviation of solutions desired (fields of deviation for potential, electric field strength, and strain field) as compared to corresponding solution for composites of ideal periodic structure. We discuss some approximate approaches for these fields of deviation, namely, the first approximation (or correlative approximation), the singular approximation, and the generalized singular approximation. We obtain analytic solutions for a tensor of effective elastic permeability, a tensor of piezo-mechanical permeability, and a tensor of dielectric permeability of quasi-periodic composites. These relationships are presented in terms of known solutions for ideally periodic structures, a medium of statistical mixture type, and structural parameters of quasi-periodic structure (tensors of anisotropy of disorder and a coefficient of periodicity). We present some numerical results for effective moduli of transversally isotropic piezo-ceramics PZT-4 with spherical pores.