We theoretically investigated excitonic states, energy and oscillator strength of optical transitions in GaN quantum dots characterized by different size, shape, interface, and substrate. On the basis of our multi-band model we determined that the piezoelectric field-induced red shift of the ground state transition, observed in recent experiments, can manifest itself only in strained GaN/AIN dots with the dot height larger than 3 nm. It was also established that the oscillator strength of the red-shifted transitions is small (< 0.05) and decreases fast with increasing the dot size, while the strength of ground state transitions in c-GaN/c-AIN and GaN/dielectric dots is large (approximately 0.4-0.7) and almost independent of the dot size.