Scintillators with pulse-shape discrimination (PSD) capability are of great interest to many fields in the scientific community. The ability to discern a gamma ray from a neutron using PSD varies between different types of scintillator materials and dopants. A new generation of organic scintillator materials with PSD capability were studied to determine their radiation hardness to ionizing and non-ionizing radiation. The PSD capability, average pulse shapes, and light output of four types of organic scintillator were characterized before and after neutron and gamma-ray irradiation. The main goal of this investigation is to study the effects of long-term irradiation that may be experienced in space applications on the light output and particle discriminating capabilities of each material. EJ-270, EJ-276, organic glass, and Stilbene were tested. Damage due to non-ionizing (neutron) radiation was not observed in any of the scintillators up to $2.56\times10^{11}$ n/cm$^2$, except for Stilbene which showed a small (12$\%$) decrease in light output. All scintillators presented some light output reduction after ionizing (gamma-ray) irradiation, with reductions of 17$\%$ (EJ-276 and OGS), 32$\%$ (EJ-270), and 42$\%$ (Stilbene) observed immediately after 100 kRad.