A comprehensive experimental and theoretical investigation was performed for the system of As-Sb nanoclusters and nanoscale dislocation loops in GaAs:Sb films grown by molecular beam epitaxy at low temperature and subsequently annealed. A model was developed for the elastic stress relaxation, self-energies and interactions in such cluster-loop nanosystems. The model was based on the experimental investigation of the microstructure of the As-Sb nanoclusters by transmission electron microscopy. The atomic structures of the As-Sb nanoclusters and dislocation loops, as well as their orientation relationships were determined. A strong anisotropic mismatch between the As-Sb nanoclusters and GaAs matrix has been revealed. This mismatch was proven to be a reason for the formation of the prismatic nanoscale dislocation loops nearby the nanoclusters. Our theoretical model explores the elastic properties of an inclusion with uniaxial dilatation. For such inclusions, the elastic stresses and stored energy are determined in a closed analytical form. The theoretical analysis predicts a specific non-linear dependence of the dislocation loop diameter on the cluster diameter, which fits well the experimentally observed one. It is demonstrated that both the change in the inclusion self energy due to diminishing dilatation and the interaction between the dislocation loop and inclusion are important in the relaxation phenomena at stressed nanoscale inclusions in semiconductors.