We investigated the size and crystal structure of nanometer-sized ω inclusions in single crystals of β-Ti alloys by X-ray diffraction pole-figure measurements and reciprocal space mapping. We studied the topotactical relation of the β and ω crystal lattices, and from the positions and shapes of the diffraction maxima of the ω lattice determined the mean size of the ω inclusions and the misfit of the inclusion lattice with respect to the host lattice, as well as their changes during ageing. The lattice of the ω inclusions exhibits a large positive misfit already before ageing and the misfit is subsequently reduced during the ageing process. Using the theories of elasticity and X-ray scattering we simulated diffuse X-ray scattering around the β diffraction maxima and demonstrated that the diffuse scattering is caused mainly by local elastic strains in the β host phase around the ω inclusions.