Determining the in situ 3D nano- and microscale strain and reorientation fields in hierarchical nanocomposite materials is technically very challenging. Such a determination is important to understand the mechanisms enabling their functional optimization. An example of functional specialization to high dynamic mechanical resistance is the crustacean stomatopod cuticle. Here we develop a new 3D X-ray nanostrain reconstruction method combining analytical modelling of the diffraction signal, fibre-composite theory and in situ deformation, to determine the hitherto unknown nano- and microscale deformation mechanisms in stomatopod tergite cuticle. Stomatopod cuticle at the nanoscale consists of mineralized chitin fibres and calcified protein matrix, which form (at the microscale) plywood (Bouligand) layers with interpenetrating pore-canal fibres. We uncover anisotropic deformation patterns inside Bouligand lamellae, accompanied by load-induced fibre reorientation and pore-canal fibre compression. Lamination theory was used to decouple in-plane fibre reorientation from diffraction intensity changes induced by 3D lamellae tilting. Our method enables separation of deformation dynamics at multiple hierarchical levels, a critical consideration in the cooperative mechanics characteristic of biological and bioinspired materials. The nanostrain reconstruction technique is general, depending only on molecular-level fibre symmetry and can be applied to the in situ dynamics of advanced nanostructured materials with 3D hierarchical design.