Defect properties of quaternary GaNAsP/GaP epilayers grown by vapor phase epitaxy (VPE) are studied by photoluminescence and optically detected magnetic resonance techniques. Incorporation of more than 0.6% of nitrogen is found to facilitate formation of several paramagnetic defects which act as competing carrier recombination centers. One of the defects (labeled as Ga-i-D) is identified as a complex defect that has a Ga interstitial (Ga-i) atom residing inside a Ga tetrahedron as its core. A comparison of Ga-i-D with other Ga-i-related defects known in ternary GaNP and GaNAs alloys suggests that this defect configuration is specific to VPE-grown dilute nitrides.