Centrifugal pumps are essential in many industrial processes. An accurate operation diagnosis of centrifugal pumps is crucial to ensure their reliable operation and extend their useful life. In real industry applications, many centrifugal pumps lack flowmeters and accurate pressure sensors, and therefore, it is not possible to determine whether the pump is operating near its best efficiency point (BEP). This paper investigates the detection of off-design operation and cavitation for centrifugal pumps with accelerometers and current sensors. To this end, a centrifugal pump was tested under off-design conditions and various levels of cavitation. A three-axis accelerometer and three Hall-effect current sensors were used to collect vibration and stator current signals simultaneously under each state. Both kinds of signals were evaluated for their effectiveness in operation diagnosis. Signal processing methods, including wavelet threshold function, variational mode decomposition (VMD), Park vector modulus transformation, and a marginal spectrum were introduced for feature extraction. Seven families of machine learning-based classification algorithms were evaluated for their performance when used for off-design and cavitation identification. The obtained results, using both types of signals, prove the effectiveness of both approaches and the advantages of combining them in achieving the most reliable operation diagnosis results for centrifugal pumps.