Anaerobic mono- and co-digestion of two municipal sludge wastes (A and C), grease trap waste (B), and meat processing waste (D) were investigated under mesophilic temperature conditions by biochemical methane potential (BMP) assays and kinetic modeling. Wastes ratios in the mixtures were systematically selected based on Simplex Lattice mixture design, and statistical analyses were performed to elucidate possible synergetic and antagonistic effects of wastes interactions on the kinetics and ultimate methane potentials of wastes co-digestion. The mixture of 1/8A + 1/8B + 1/8C + 5/8D (VS basis) showed the highest COD and VS removals of 35.0% and 33.8%, respectively. Substrates B and D with 980 and 641 mL/g-VS methane yields, respectively, had the highest BMP. However, with reaction rate constants of 0.047 and 0.070 d−1, their methane production was very slow. It was observed that diluting these organic-rich but complex substrates with readily soluble wastes (A and C) enhanced their biogas production rate markedly. Statistical analysis showed that the interactions among the substrates in co-digestion did not have a significant impact on the ultimate cumulative methane yields. Nevertheless, these interactions proved to have synergic and antagonistic effects on the reaction rates, leading to accelerated or hindered methane production rates. As a result, while the methane yield of wastes co-digestion could be predicted by proportional summation of methane yields obtained in mono-digestions of these waste fractions, such linear regressions were unable to provide a good estimation of the rate constants. Quadratic equations, however, were found to estimate the rate constants of the co-digestion process with good accuracy