First principles calculations based on the nonlocal density approximation to the density functional theory were performed to study structures, stabilities, and vibrational properties of small (monomer, triatomic, and dimer) neutral and ionized clusters of AlN, GaN, and InN. As a general trend, triatomic isomers prefer doubler spin states, whereas triplets are predicted for the monomer and the linear dimer clusters. Both nitrogen-excess and metal-excess triatomic clusters show minimum energy configurations to be approximately linear. The most stable isomer of Al2N2 and Ga2N2 is a rhombus with a singlet spin state, though In2N2 is predicted not to be stable against dissociation into In-2 and N-2. A strong dominance of the N-N bond over the metal-nitrogen and metal-metal bonds appears to control the structural skeletons and the chemistry of these clusters. This is manifested in the dissociation of neutral and singly-ionized clusters, where the loss of metal atoms is shown to be the most likely fragmentation channel, except in the case of the dimer, in which the formation of two homonuclear diatomics is favored. The vibrational modes and frequencies are also explained in terms of the different bond strengths found in the diatomic clusters.