The nutrient availability of carbon (C), nitrogen (N), and phosphorus (P) has been decreasing due to a decline in the biological function of yellow soil, limiting potato yield (PY). Increasing biochar or organic fertilizer input is an effective way to improve soil microbiological fertility. However, indexes to regulate soil microbiological fertility using biochar and organic fertilizer individually or in combination and these indexes’ associations with PY remain unclear. In this study, four fertilization strategies were developed using the nutrient balance method: CK (recommended NPK fertilization), BC (NPK + biochar), OF (NPK + organic fertilizer), and BF (NPK + 1/2 biochar + 1/2 organic fertilizer). Using different fertilization strategies, the eco-stoichiometry characteristics of the soil microbial biomass and enzyme activity; the bioavailability of C, N, and P; and the differences in PY were investigated, and the direct and indirect effects of these factors on PY were determined over a two-year period. The results showed that exogenous organic matter input could considerably affect the stoichiometric ratios of soil microbial biomass; C; N; P; the stoichiometric ratios of C-converting, N-converting, and P-converting enzyme activities (expressed as BG+CBH, NAG+LAP, and AP, respectively); and the integrated enzyme index (IEI). The IEI was the highest in BF, followed by OF, BC, and CK. A significant positive correlation was found between the microbial biomass C, N, and P and their corresponding converting enzyme activities (p < 0.05). The ln(BG+CBH):ln(NAG+LAP), ln(BG+CBH):lnAP, and ln(NAG+LAP):lnAP ratios were all higher than 1:1, but they approached 1:1 in the order of CK-BC-OF-BF. Compared to soil C and N, P-converting enzyme activity was the primary limiting factor for soil nutrient conversion in the study area. BF was less restricted by P and more balanced in its nutrient ratio. The microbial biomass C:N:P could affect PY in eight ways. (1) Microbial biomass C:N directly decreased PY, and microbial biomass C:P indirectly increased PY. (2) It could decrease C-converting enzyme activity, (3) decrease N availability to increase C-converting enzyme activity, (4) decrease P availability, or (5) decrease P availability to decrease the soil C:P-converting enzyme activity ratio. Microbial biomass N:P indirectly increased PY (6) by increasing the soil C:P-converting enzyme activity ratio, (7) by increasing C-converting enzyme activity, or (8) by increasing N availability to increase C-converting enzyme activity. Thus, BF is an effective strategy for regulating the soil microbiological fertility index; enhancing C, N, and P nutrient conversion; and increasing PY. The input of exogenous organic matter can alter the stoichiometric ratios of soil microbial biomass C, N, and P; the stoichiometric ratios of C-converting, N-converting, and P-converting enzyme activities; and nutrient availability, thus regulating PY. Microbial biomass N:P and soil C:P-converting enzyme activity ratios influence PY the most.