Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interactions (MRCI) calculations are made on the electronic states of P3, As3, Sb3, Bi3 and all their positive ions. All group V trimers have Jahn-Teller distorted 2A2 ground states arising from the 2E" (D3h) state while the positive ions have 1A'1 (D3h) equilateral-triangular ground states. For the neutral species, the 2B1 Jahn-Teller component was found to be nearly degenerate with the 2A2 component. Extensive studies on As3, Sb3, and Bi3 reveal the existence of 4A"2, 4E', and 2E' (D3h) excited states which also undergo Jahn-Teller distortion. The binding energies and the ionization potentials (IP) of all group V trimers were computed and compared with known experimental data on some of these species. The IPs and the binding energies per atom of group V trimers were found to be significantly smaller than dimers thus exhibiting odd-even alternation in these properties. Our computations explain the dramatically different photofragmentation patterns for antimony and bismuth clusters observed by Geusic et al.