Heterostructure n-GaAs/InGaP/p-GaAs core-multishell nanowire diodes are synthesized by metal-organic vapor-phase epitaxy. This structure allows a reproducible, selective wet etching of the individual shells and therefore a simplified contacting of single nanowire p-i-n junctions. Nanowire diodes show leakage currents in a low pA range and at a high rectification ratio of 3500 (at +/- 1V). Pronounced electroluminescence at 1.4 eV is measured at room temperature and gives evidence of the device quality. Photocurrent generation is demonstrated at the complete area of the nanowire p-i-n junction by scanning photocurrent microscopy. A solar-conversion efficiency of 4.7%, an open-circuit voltage of 0.5 V and a fill factor of 52% are obtained under AM 1.5G conditions. These results will guide the development of nanowire-based photonic and photovoltaic devices.