Inconel 800H superalloy is a difficult-to-turn material. This study aims to achieve optimal machining results, including reduced cutting force, improved surface roughness, and minimized residual stress, by optimizing input machining parameters like cutting speed, feed rate, spraying angle, and nozzle distance on Inconel 800H. The Taguchi L27 method is utilized for experimentation, while the Harris hawks optimizer (HHO) is applied in a multi-objective optimization model. Additionally, the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS) is used to identify the optimal input parameters. Five distinct weight schemes were employed, including the Analytic Hierarchy Process (AHP), the Entropy weight method, Criteria Importance through Inter-Criteria Correlation (CRITIC), Grey relational analysis (GRA), and Principal Component Analysis (PCA) to determine response weights. The analysis revealed that the primary factor affecting all measured weights is the feed rate, with the nozzle angle closely followed, as determined by ANOVA, based on a comprehensive evaluation of all output responses. Notable enhancement in MQL turning when contrasted with dry turning, reflected in the output responses of roughness, force, and residual stress at 72.62%, 8.08%, and 19.32%, respectively, using AHP-TOPSIS compared to AHP-HHO.