Contribution to the damping of inter-area and torsional oscillation modes, in doubly fed induction generators (DFIG) based wind farms, by power oscillation damping controllers (PODCs) based on two conventional structures and a fuzzy control strategy is investigated in this study. In this regard, a PODC with no lead/lag compensation is designed first and then a PODC with one lead/lag block is developed using eigenvalue techniques and the application of an iterative process based on the bat optimisation algorithm (BOA). Moreover, a fuzzy PODC, based on a simple fuzzy controller and tuned with the BOA according to the system transient response under a critical perturbation, is also designed. Comparative performance of the three PODCs is evaluated on a multi-machine power system. It is observed that all three PODCs can contribute to improving the damping of inter-area oscillations. However, eigenvalue analysis and non-linear time domain simulations reveal that each of them may also impact to a lesser or greater extent the shaft torsional oscillation mode damping. Their relative impact in this regard is also investigated.