Developing automatic algorithms for real-time monitoring of underwater acoustic events is essential in ocean acoustic applications. Most previous ocean acoustic ecosystem monitoring studies are non-real-time, focusing on data received on a single hydrophone or a specific analysis, such as bearing estimation or detection, without considering the full end-to-end analysis system. Here, we develop a unified framework for real-time ocean acoustic data analysis including beamforming, detection, bearing estimation, and classification of transient underwater acoustic events. To detect sound sources, thresholding on computed mel-scale per-channel energy normalization (PCEN) is applied, followed by morphological image opening to extract pixels with significant intensities. Next, connected component analysis is applied for grouping pixel detections. The bearing of signal detections is next estimated via nonmaximum suppression (NMS) of 3-D stacked beamformed spectrogram imageries. To classify a variety of whale species from their calls, time-frequency features are extracted from each detected signal's beamformed power spectrogram. These features are next applied to train three classifiers, including support vector machine (SVM), neural networks, and random forest (RF), to classify six whale vocalization categories: Fin, Sei, Unidentified Baleen, Minke, Humpback, and general Odontocetes. Best results are obtained with the RF classifier, which achieved 96.7% accuracy and 87.5% F1 score. A variety of accelerating approaches and fast algorithms are implemented to run on GPU. During an experiment in the U.S. Northeast coast in September 2021, the software and hardware advances developed here were used for near real-time analysis of underwater acoustic data received by Northeastern University's in-house fabricated 160-element coherent hydrophone array system.