Structures and thermodynamic properties of the imidogallanes [HGaNH] _n with high oligomerization degrees n = 7-16 and related amido-imido compounds have been investigated theoretically at the B3LYP level of theory with all-electron pVDZ and effective core potential LANL2DZ(d,p) basis sets. Needle-shaped oligomers which violate the "isolated square rule" were found to be more stable than cage isomers. The needle-shape oligomer with n = 16 is predicted to be exceptionally stable at low temperatures. Octamer and hexamer clusters dominate the gas phase at higher temperatures. The highest oligomerization degree of the spontaneous cluster formation has been estimated. It is concluded that generation of the gas-phase [HGaNH]_n clusters with oligomerization degree n ≥ 60 is viable. This makes these species possible intermediates involved in the gas-phase generation of GaN nanoparticles. A case study of methyl-substituted analogues suggests that formation of the gaseous [MeGaNH]_n oligomers is even more favorable compared to that of [HGaNH]_n. We predict that spontaneous growth of GaN oligomers is favorable thermodynamically. Laser-assisted generation of GaN nanorods at low-temperature conditions appears to be feasible.