Greenhouse gas emissions from agricultural production systems are a major area of concern in mitigating climate change. Therefore, a study was conducted to investigate the effects of crop residue, nutrient management, and soil moisture on methane (CH4) emissions from maize, rice, soybean, and wheat production systems. In this study, incubation experiments were conducted with four residue types (maize, rice, soybean, wheat), seven nutrient management treatments {N0P0K0 (no nutrients), N0PK, N100PK, N150PK, N100PK + manure@ 5 Mg ha−1, N100PK + biochar@ 5 Mg ha−1, N150PK+ biochar@ 5 Mg ha−1}, and two soil moisture levels (80% FC, and 60% FC). The results of this study indicated that interactive effects of residue type, nutrient management, and soil moisture significantly affected methane (CH4) fluxes. After 87 days of incubation, the treatment receiving rice residue with N100PK at 60% FC had the highest cumulative CH4 mitigation of −19.4 µg C kg−1 soil, and the highest emission of CH4 was observed in wheat residue application with N0PK at 80% FC (+12.93 µg C kg−1 soil). Nutrient management had mixed effects on CH4 emissions across residue and soil moisture levels in the following order: N150PK > N0PK > N150PK + biochar > N0P0K0 > N100PK + manure > N100PK + biochar > N100PK. Decreasing soil moisture from 80% FC to 60% FC reduced methane emissions across all residue types and nutrient treatments. Wheat and maize residues exhibited the highest carbon mineralization rates, followed by rice and soybean residues. Nutrient inputs generally decreased residue carbon mineralization. The regression analysis indicated that soil moisture and residue C mineralization were the two dominant predictor variables that estimated 31% of soil methane fluxes in Vertisols. The results of this study show the complexity of methane dynamics and emphasize the importance of integrated crop, nutrient, and soil moisture (irrigation) management strategies that need to be developed to minimize methane emissions from agricultural production systems to mitigate climate change.