Global shocks potentially distort economy’s achieved equilibria. Considering the 2020 global crude oil price shock and the 2019 coronavirus disease pandemic, this study proposes an energy and environment integrated general equilibrium model to analyze the economic, energy, and environmental effects of these global shocks on Nigeria, a developing, oil-producing, oil-dependent, and oil-exporting country. Furthermore, the mitigating roles of a fiscal stimulus–response package (palliative) are investigated and analyzed. Generally, the developed model predicts a decline in the level of economic activities. The study results are unsurprising due to Nigeria’s heavy reliance on crude oil. However, sectorial-specific impacts exist as some sectors experience output declines while others do not. Environmental quality is improved since more carbon is abated, nonetheless. Carbon intensities increased given that the price effects outweighed the quantity effects— reduced emission results from reduced economic activities and not from technological progress. The results further show a revenue-abatement paradox; a fixed carbon tax approach minimizes the tax revenue loss but may discourage carbon abatement. Conversely, the ad valorem and specific carbon tax systems encourage carbon abatement but reduce carbon tax revenues. The government’s fiscal policy stimulus–response (palliative) action dampens the impact of these global shocks on both the domestic agents and the overall economy. The results are robust and can be applied to the experiences of other developing oil-producing, oil-exporting, and oil-dependent economies.