Nanowires (NWs) based on ternary GaAsP and quaternary GaNAsP alloys are considered as very promising materials for optoelectronic applications, including in multi-junction and intermediate band solar cells. The efficiency of such devices is expected to be largely controlled by grown-in defects. In this work we use the optically detected magnetic resonance (ODMR) technique combined with photoluminescence measurements to investigate the origin of point defects in Ga(N)AsP NWs grown by molecular beam epitaxy on Si substrates. We identify gallium vacancies, which act as non-radiative recombination centers, as common defects in ternary and quaternary Ga(N)AsP NWs. Furthermore, we show that the presence of N is not strictly necessary for, but promotes, the formation of gallium vacancies in these NWs.