We report on the inelastic response of AV 2 Al 20 (with A = Sc, La and Ce) probed by high-resolution inelastic neutron scattering experiments. Intense signals associated with the dynamics of Sc, La and Ce are identified in the low-energy range at 6-14 meV in ScV 2 Al 20 and at 8-16 meV in LaV 2 Al 20 and CeV 2 Al 20 . Their response to temperature changes between 2 and 300 K reveals a very weak softening of the modes upon heating in LaV 2 Al 20 and CeV 2 Al 20 and a distinguished blue shift by about 2 meV in ScV 2 Al 20 . By means of density functional theory (DFT) and lattice dynamics calculations (LDC) we show that the unusual anharmonicity of the Sc-dominated modes is due to the local potential of Sc featured by a strong quartic term. The vibrational dynamics of ScV 2 Al 20 as well as of LaV 2 Al 20 and CeV 2 Al 20 is reproduced by a set of eigenmodes. To screen the validity of the DFT and LDC results they are confronted with data from X-ray diffraction measurements. The effect of the strong phonon renormalization in ScV 2 Al 20 on thermodynamic observables is computed on grounds of the LDC derived inelastic response. To set the data in a general context of AV 2 Al 20 compounds and their physical properties we report in addition computer and experimental results of the binary V 2 Al 20 compound. Neutron spectroscopy and ab initio calculations indicate the apparent glass-like lattice thermal conductivity κ l of the nano-cage compound ScV 2 Al 20 as an effect of phonon renormalization predetermined by the crystal's ground state properties.