Exceptional water retention properties make compacted clays and clayrocks attractive materials in waste management applications, e.g. as buffer materials and barrier formations for radionuclide release in geological disposal of spent nuclear fuel elements. Consisting of particles with a very high aspect ratio, clay materials exhibit significant structural anisotropy with potential implications on their performance. In this work, the micron-scale and nanometer-scale anisotropy in compacted calcium montmorillonite and MX-80 bentonite were investigated and quantified under varying humidity conditions; the utilized novel experimental method combines X-ray microtomography (XMT) and small-angle X-ray diffraction to near-simultaneously characterize both the micron-scale 3D morphology and mineralogical properties such as clay platelet spacing in platelet stacks (tactoids) and tactoid orientation. Sedimentation during the purification process and lack of accessory minerals were found to induce much stronger orientation in purified Ca-montmorillonite as compared to the MX-80. In highly anisotropic samples, the orientation of microcracks visualized with XMT under low humidity conditions was found to correlate with the local orientation of clay tactoids measured with X-ray diffraction. The proposed experimental method can be applied to a wide range of similar materials, such as shales or samples from clayrock formations.