Alloying group IV semiconductors offers an effective way to engineer their electronic properties and lattice dynamics. The incorporation of Sn in Ge permits a transition from an indirect to a direct bandgap semiconductor. Here, by combining polarization, laser power-dependent and temperature-dependent micro-Raman spectroscopy we explore the full lattice dynamics of Ge1-xSnx (x = 0.01, 0.06 and 0.08) alloy nanowires. In the high Sn content samples (x = 0.06), a low-frequency tail and a high-frequency shoulder are observed which are associated with the F2g optical phonon mode of Ge (Ge-Ge mode). The new modes are assigned to the stretching of Ge-Ge bonds due to Sn-induced lattice relaxation and compression, respectively. The symmetry of the observed Raman modes has been studied by polarization-dependent Raman scattering. Nonlinear fitting of the laser power-dependent intensity of the high-frequency Ge-Ge mode in the Ge1-xSnx alloy nanowires with x = 0.06 and 0.08 suggests the activation of a third-order stimulated Raman scattering process, due to the high intensity localized electric field surrounding the Sn clusters. Finally, from the temperature-dependent Raman study, we have estimated the isobaric Grüneisen parameters for all the observed modes.