In light of the stochastic nature of wind, the main obstacle to reliable penetration of wind power into the power grid is its variability. An accurate multi-step prediction of wind power is the most efficient way to address this issue, along with challenges in wind power management and maintenance. Several strategies have been presented in the literature for multi-step ahead wind power prediction, however, a comprehensive comparison of these strategies has not been performed to determine how outliers in power datasets influence the accuracy of multi-step ahead predictions at different forecasting horizons. To fill this gap, in this study, by reviewing the existing strategies, three main approaches including the recursive, direct, and multi-input multi-output (MIMO) strategies are investigated using two real-world datasets from two wind turbines in Turkey and Scotland. A hybrid prediction method based on application of the Isolation Forest for outlier treatment, long short-term memory (LSTM) as the core of the prediction model and a new hyperparameter optimization algorithm for the tuning of the LSTM model is used for predictions in different strategies. According to the results of the experiments (1) in two-step ahead wind power forecasting, all strategies produce similar results, in both wind turbines; (2) in all forecast horizons of more than two steps ahead, the MIMO approach is best when the dataset does not contain any outliers – however, when there are outliers, the direct approach performs better; (3) in both datasets, the recursive approach to wind power forecasting produces the highest error rates.