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The crystal structure and magnetic correlations in triangular antiferromagnet FeGa$_2$S$_4$ are studied by x-ray diffraction, magnetic susceptibility, neutron diffraction and neutron inelastic scattering. We report significant mixing at the cation sites and disentangle magnetic properties dominated by major and minor magnetic sites. The magnetic short-range correlations at 0.77 \AA$^{-1}$ correspond to the major sites and being static at base temperature they evolve into dynamic correlations around 30 - 50 K. The minor sites contribute to the magnetic peak at 0.6 \AA$^{-1}$, which vanishes at 5.5 K. Our analytical studies of triangular lattice models with bilinear and biquadratic terms provide the ratios between exchanges for the proposed ordering vectors. The modelling of the inelastic neutron spectrum within linear spin wave theory results in the set of exchange couplings $J_1=1.7$\,meV, $J_2=0.9$\,meV, $J_3=0.8$\,meV for the bilinear Heisenberg Hamiltonian. However, not all features of the excitation spectrum are explained with this model.