The binary GeySnz and ternary SixGeySnz molecular systems containing up to five atoms were investigated by means of density functional theory and coupled cluster calculations. The minimum energy structures were calculated and higher energy isomers are also proposed. The atomization energies of the ground state isomers were calculated by the CCSD(T) method with correlation consistent basis sets up to quadruple-zeta quality. The resulting values were extrapolated to the complete basis set limit and corrected by an approximate evaluation of the spin-orbit effect. Energetic properties such as binding, fragmentation and mixing energies, and HOMO-LUMO gap were analyzed as a function of the cluster size and composition. By using empirically adjusted atomization energies and DFT harmonic frequencies, the thermal functions were evaluated, and a thermodynamic database for the Si-Ge-Sn system was built, containing data for 55 gaseous species. On this basis, equilibrium calculations were performed in the temperature interval 1600-2200 K aimed at predicting the composition of the gas phase under various conditions. The results presented here can be of interest to improve the microscopic knowledge of Ge-Sn and Si-Ge-Sn materials, which are among the most promising candidates for advanced applications in the field of electronic and optoelectronic components, both as epitaxially grown layers and as nanocrystal quantum dots.