We elucidate the atomistic level details of the formation of 1-D GaN nanostructures on Si(001) by molecular beam epitaxy. In a multitechnique study, we understand the epitaxy and role of the unintentional interfacial SiNx layer in determining the shape, structure, and organization of the nanofeatures. The 1-D GaN features are seen to be m-faceted and grow along the Si(111) planes and thus are tilted with a 4-fold symmetry on the cubic Si(100) surface. The interfacial mismatch induced dislocations are shown to provide the nucleation centers for the spiral 1-D growth, while their local density determines their evolution into solid rods, tubes, or c-tubes. The unintentional interfacial nitridation of the substrate forms discontinuous amorphous mounds that provide the epitaxial contact to the substrate and also laterally isolate the rods/tubes, enabling them to grow laterally in their equilibrium hexagonal wurtzite structures. We consolidate the results into a schematic model to unveil the underlying mechanism and demonstrate the subtle relationship between the kinetics of growth and the interfacial properties.