While conventional X-ray crystallography has been extensively used to determine atomic structure, its applicability is limited to objects than can be formed into large crystal samples. An appealing alternative, made possible by recent advances in light source technology, is X-ray nanocrystallography, which is able to image structures resistant to large crystallization by substituting a large ensemble of easier to build nanocrystals, which are delivered to an X-ray beam via a liquid jet. However, nanocrystallographic diffraction experiments suffer from severe shot-to-shot variability due to varying crystal sizes, orientations, and incident photon flux densities and the diffraction images are highly corrupted with noise. Autoindexing techniques, commonly used in conventional crystallography, can determine partial orientation information using Bragg peak patterns, but only up to crystal lattice symmetry. This limitation results in an ambiguity in the orientations, known as the indexing ambiguity, when the diffraction data displays less symmetry than the lattice and leads to data that appear twinned if left unresolved. Furthermore, missing phase information must be recovered to determine the imaged object's structure. An algorithmic framework is presented that utilizes a periodic analysis of both Bragg and non-Bragg data for precise autoindexing, Fourier analysis and image segmentation to reveal crystal size, multi-modal analysis coupled with scaling to correct for varying incident photon flux densities and identify structure factors, and clique analysis on a graph theoretical model of concurrency to resolve the indexing ambiguity. Additionally, the feasibility of determining structure through iterative phasing techniques, which have less experimental requirements than traditional phasing methods, is examined. Results are presented for several sets of simulated nanocrystallographic diffraction images using typical parameters and noise levels reported in current experiments.