The electronic structure of defects produced by 2.5-MeV electron irradiation and their effect on optical properties of GaN are investigated using photoluminescence (PL) and optically detected magnetic resonance (ODMR) techniques. The electron irradiation is shown to produce, in particular, a deep PL band with a no-phonon line at around 0.88 eV followed by a phonon-assisted sideband. We suggest that this emission is caused by an internal transition between excited and ground state of a deep defect. The excited state is a multiple-level state, as revealed from temperature dependent PL and level anti-crossing experiments. The electronic structure of the 0.88 eV defect is shown to be sensitive to the internal strain in the GaN epilayers. The ODMR studies reveal that the principal axis of the defect coincides with the c-axis of the host lattice and should therefore be either an on-site point defect or an axial complex defect along the c-axis.