In this research, a thermodynamic study is executed for a multi-generation hybrid renewable energy system (MG-HRES) for off-grid energy supply to a rural settlement in Katsina state, Nigeria. In the system, a downdraft biomass gasifier (BMG), syngas electrical engine (SGE) attached with an absorption refrigeration system and wind turbine generator are integrated to relieve wind variability and deliver three useful outputs. The integrated system, which is sized to supply the average electricity load of 2000 dwellings, is modelled and analysed thermodynamically through Matlab computer code. The overall energetic and exergetic efficiencies are 0.48 and 0.25, respectively, with hot water and cooling outputs of 130 and 393 kW. To ascertain the quantities and locations of irreversibility within the MG-HRES, exergy destruction analysis is deployed to scrutinise the thermodynamics process in every part of the system. The major exergy destruction of about 95% of the total cycle irreversibility occurs in the BMG, followed by SGE, 3%. The variation of exergy destruction, exergy and energy efficiency for the MGHRES and its constituents are determined against fluctuations in the exhaust temperature, capacity factor, load factor and reference temperature of the environment.