Core-shell nanowires (NWs) with asymmetric shells allow for strain engineering of NW properties because of the bending resulting from the lattice mismatch between core and shell material. The bending of NWs can be readily observed by electron microscopy. Using X-ray diffraction analysis with a micro- and nano-focused beam, the bending radii found by the microscopic investigations are confirmed and the strain in the NW core is analyzed. For that purpose, a kinematical diffraction theory for highly bent crystals is developed. The homogeneity of the bending and strain is studied along the growth axis of the NWs, and it is found that the lower parts, i.e. close to the substrate/wire interface, are bent less than the parts further up. Extreme bending radii down to similar to 3 mu m resulting in strain variation of similar to 2.5% in the NW core are found.