III-As nanowires are candidates for near-infrared light emitters and detectors that can be directly integrated onto silicon. However, nanoscale to microscale variations in structure, composition, and strain within a given nanowire, as well as variations between nanowires, pose challenges to correlating microstructure with device performance. In this work, we utilize coherent nanofocused X-rays to characterize stacking defects and strain in a single InGaAs nanowire supported on Si. By reconstructing diffraction patterns from the 21̅1̅0 Bragg peak, we show that the lattice orientation varies along the length of the wire, while the strain field along the cross-section is largely unaffected, leaving the band structure unperturbed. Diffraction patterns from the 011̅0 Bragg peak are reproducibly reconstructed to create three-dimensional images of stacking defects and associated lattice strains, revealing sharp planar boundaries between different crystal phases of wurtzite (WZ) structure that contribute to charge carrier scattering. Phase retrieval is made possible by developing multiangle Bragg projection ptychography (maBPP) to accommodate coherent nanodiffraction patterns measured at arbitrary overlapping positions at multiple angles about a Bragg peak, eliminating the need for scan registration at different angles. The penetrating nature of X-ray radiation, together with the relaxed constraints of maBPP, will enable the in operando imaging of nanowire devices.