Man-made organic waste leads to the rapid proliferation of pollution around the globe. Effective bio-waste management can help to reduce the adverse effects of organic waste while contributing to the circular economy at the same time. The toxic oily-biological sludge generated from oil refineries' wastewater treatment plants is a potential source for biogas energy recovery via anaerobic digestion. However, the oily-biological sludge's carbon/nitrogen (C/N) ratio is lower than the ideal 20-30 ratio required by anaerobic digestion technology for biogas production. Sugarcane bagasse can be digested as a high C/N co-substrate while the oily-biological sludge acts as a substrate and inoculum to improve biogas production. In this study, the best C/N with co-substrate volatile solids (VS)/inoculum VS ratios for the co-digestion process of mixtures were determined empirically through batch experiments at temperatures of 35-37 degrees C, pH (6-8) and 60 rpm mixing. The raw materials were pre-treated mechanically and thermo-chemically to further enhance the digestibility. The best condition for the sugarcane bagasse delignification process was 1\% (w/v) sodium hydroxide, 1:10 solid-liquid ratio, at 100 degrees C, and 150 rpm for 1 h. The results from a 33-day batch anaerobic digestion experiment indicate that the production of biogas and methane yield were concurrent with the increasing C/N and co-substrate VS/inoculum VS ratios. The total biogas yields from C/N 20.0 with co-substrate VS/inoculum VS 0.06 and C/N 30.0 with co-substrate VS/inoculum VS 0.18 ratios were 2777.0 and 9268.0 mL, respectively, including a methane yield of 980.0 and 3009.3 mL, respectively. The biogas and methane yield from C/N 30.0 were higher than the biogas and methane yields from C/N 20.0 by 70.04 and 67.44\%, respectively. The highest biogas and methane yields corresponded with the highest C/N with co-substrate VS/inoculum VS ratios (30.0 and 0.18), being 200.6 mL/g VSremoved and 65.1 mL CH4/g VSremoved, respectively.