The functional properties of materials are closely related to their structure and composition. In this work, the relationship between the local atomic structure and thermochromic properties of copper molybdate (CuMoO4) and its solid solutions with tungsten and zinc (CuMo1-xWxO4 and Cu1-xZnxMoO4) is studied using X-ray absorption and resonant X-ray emission spectroscopy (XAS and RXES) methods. Experimental data are interpreted based on reverse Monte Carlo modelling and theoretical calculations. The study demonstrates the possibilities of the XAS and RXES techniques to probe the local structure changes in materials with low symmetry, as well as explains the relationship between the local structure distortions and lattice dynamics of the considered materials and their thermochromic properties.