Ultrasonic wave propagation through a two-dimensional nonreciprocal phononic crystal with asymmetric aluminum rods in viscous water is studied for its application in Anderson localization and trapping of acoustic energy. A one-dimensional disorder in the otherwise 2D periodic crystal is introduced by disorienting the asymmetric rods along the rows and by keeping them equally oriented along the columns. An exponential decay of sound waves travelling along the direction of disorder is observed demonstrating Anderson localization whereas sound propagates as extended wave along the ordered direction. Localization length for the case of strong disorder with high randomness in the orientation of rods and weak disorder with weak fluctuations in the orientation of rods is evaluated. The degree of randomness in the orientation of the rods controls the localization length of the wave. Thouless's theoretical prediction for the scaling of Lyapunov exponent with disorder is experimentally observed for weak disorder at frequency in the transmission band and anomalous scaling is observed for band edge frequency. Transmission spectra of acoustic waves is also measured for opposite direction of propagation and nonreciprocity is observed for the exponentially weak transmission in the disordered direction as well as for extended states in the ordered direction. Breaking of reciprocity in the current structure is due to the broken PT symmetry. The T symmetry or the time reversal symmetry is broken by the viscous dissipation at the boundaries of scatterers and the water, and the P symmetry is broken by the asymmetric shape of the rods. Acoustic energy trapping inside a nonreciprocal phononic crystal cavity is studied by creating three configurations of cavities. These configurations are based on the orientation of the asymmetric scatterers on each side of the cavity. Only one of these configuration utilizes the nonreciprocal property of the structure. Enhancement of energy trapping in the cavity is observed for the cavity orientation utilizing nonreciprocity. The proposed enhancement of energy trapping occurs at the transmission band frequency unlike the extensively used mechanism of energy trapping at the defect modes of the band gap of the phononic crystal. All the experimental results are verified numerically using finite element based modelling in COMSOL Multiphysics. The proposed devices can be utilized for applications in one way sound transmission, noise control, isolators, circulators and energy harvesting.