We extend optical nanometrology capabilities to smaller dimensions by using tabletop coherent extreme ultraviolet (EUV) beams. Specifically, we characterize thermal transport and acoustic wave propagation in 3D periodic silicon inverse metalattices with <15nm characteristic dimensions. Measurements of the thermal transport demonstrate that metalattices may significantly impede heat flow, making them promising candidates for thermoelectric applications. Extraction of the acoustic wave dispersion down to ~100nm shows good agreement with finite element predictions, confirming that these semiconductor metalattices were fabricated with a very high-quality. These results demonstrate that EUV nanometrology is capable of extracting both dispersion relations, and thermal properties of 3D complex nano-systems, with applications including informed design and process control of nanoscale devices.