A multimode approach based on the simultaneous application of several photothermal and photoacoustic methods is proposed for the study of thermal and thermoelastic effects in solids with residual stress. It includes photoacoustic gas microphone, photodeflection, photoreflectance and photoacoustic piezoelectric microscopy methods. This approach provides complementary information about thermal, elastic and thermoelastic properties of samples with residual stress. Some experimental results obtained within the framework of this approach for Vickers indentation zones in silicon nitride ceramic are presented. The model of the photoacoustic thermoelastic effect in solids with residual stress is proposed. It is based on the modified Murnaghan model of nonlinear elastic bodies which takes into account a possible dependence of the thermoelastic constant on stress. It is demonstrated that the developed theoretical model for the photoacoustic piezoelectric effect agrees qualitatively with the available experimental data.