Multiple switching modes in a Ta2O5/HfO2 memristor are studied experimentally and numerically through a reservoir computing (RC) simulation to reveal the importance of nonlinearity and heterogeneity in the RC framework. Unlike most studies, where homogeneous reservoirs are used, heterogeneity is introduced by combining different behaviors of the memristor units. The chosen memristor for the reservoir units is based on a Ta2O5/HfO2 bilayer, in which the conductances of the Ta2O5 and HfO2 layers are controlled by the oxygen vacancies and deep/shallow traps, respectively, providing both volatile and non-volatile resistive switching modes. These several control parameters make the second-order Ta2O5/HfO2 memristor system present different behaviors in agreement with its history-dependent conductance and allow the fine-tuning of the behavior of each reservoir unit. The heterogeneity in the reservoir units improves the pattern recognition performance in the heterogeneous memristor RC system with a similar physical structure.