The integration of functional oxides on silicon requires the use of complex heterostructures involving oxides of which the structure and properties strongly depend on the strain state and strain-mediated interface coupling. The experimental observation of strain-related effects of the individual components remains challenging. Here, a Raman scattering investigation of complex multilayer BaTiO3/LaNiO3/CeO2/YSZ thin-film structures on silicon is reported. It is shown that the Raman signature of the multilayers differs significantly for three different laser wavelengths (633, 442, and 325 nm). The results demonstrate that Raman scattering at various wavelengths allows both the identification of the individual layers of functional oxide multilayers and monitoring of their strain state. It is shown that all of the layers are strained with respect to the bulk reference samples, and that strain induces a new crystal structure in the embedded LaNiO3. Based on this, it is demonstrated that Raman scattering at various wavelengths offers a well-adapted, non-destructive probe for the investigation of strain and structure changes, even in complex thin-film heterostructures.