A new mechanism of superconductivity in high-temperature superconducting oxides (HTSCs) with partially occupied electrons in the p and d orbitals is proposed in the generalized negative U Hubbard model, including orbital degeneracy and the strong intra-atomic attraction. Our approach allows also the introduction, in a consistent way, of the orbital mixing (hybridization) between p and d bands (orbitals). The effective anisotropic Heisenberg XYZ model consisting of pseudo-orbital variables is obtained up to second order by small parameters for arbitrary concentration of particles using unitary transformation in the strong interaction limit. The ground-state energy and the partition function are obtained in the generalized mean field approximation by introducing diagonal charge-ordering parameter η and off-diagonal superconducting order parameter Δ. The self-consistent equations are analyzed and the phase diagram in the ground state and at finite temperatures for arbitrary relations between p and d bandwidths (parameter anisotropicity g) are obtained. The competition between superconducting and charge-ordering correlations for spin and orbital variables gives rise to many different pure and intermediate phases. The proposed model elucidates the role of hybridization and orbital variables on the mechanism of HTSC.