The eastern region of India, including the coastal state of Odisha, is a moderately seismic-prone area under seismic zones II and III. However, no major studies have been conducted on earthquake probability (EPA) and hazard assessment (EHA) in Odisha. This paper had two main objectives: (1) to assess the susceptibility of seismic wave amplification (SSA) and (2) to estimate EPA in Odisha. In total, 12 indicators were employed to assess the SSA and EPA. Firstly, using the historical earthquake catalog, the peak ground acceleration (PGA) and intensity variation was observed for the Indian subcontinent. We identified high amplitude and frequency locations for estimated PGA and the periodograms were plotted. Secondly, several indicators such as slope, elevation, curvature, and amplification values of rocks were used to generate SSA using predefined weights of layers. Thirdly, 10 indicators were implemented in a developed recurrent neural network (RNN) model to create an earthquake probability map (EPM). According to the results, recent to quaternary unconsolidated sedimentary rocks and alluvial deposits have great potential to amplify earthquake intensity and consequently lead to acute ground motion. High intensity was observed in coastal and central parts of the state. Complicated morphometric structures along with high intensity variation could be other parameters that influence deposits in the Mahanadi River and its delta with high potential. The RNN model was employed to create a probability map (EPM) for the state. Results show that the Mahanadi basin has dominant structural control on earthquakes that could be found in the western parts of the state. Major faults were pointed towards a direction of WNW–ESE, NE–SW, and NNW–SSE, which may lead to isoseismic patterns. Results also show that the western part is highly probable for events while the eastern coastal part is highly susceptible to seismic amplification. The RNN model achieved an accuracy of 0.94, precision (0.94), recall (0.97), F1 score (0.96), critical success index (CSI) (0.92), and a Fowlkes–Mallows index (FM) (0.95).