The traditional nonlinear energy sink (NES) exhibits high robustness over a wide frequency interval under unidirectional excitation. However, variable excitation directions and intensities are common in engineering applications, and the vibration reduction performance of the conventional NES remains uncertain. In this paper, a dynamic model of a linear oscillator (LO) equipped with an NES is established to investigate the effects of the excitation direction and intensity on the NES performance. Moreover, a three-dimensional model is designed, and a corresponding experimental platform is constructed. The vibration reduction performance of a conventional NES is theoretically investigated under variable excitation directions and intensities. Moreover, the dynamic characteristics are revealed for both free and forced vibrations. Experimental tests are conducted to validate the prediction results. This study demonstrates that the vibration suppression performance of the NES is highly sensitive to both the excitation direction and intensity. Overall, although the performance of the NES decreases with increasing excitation angle, vibration can be effectively suppressed over a wide angle range. This finding indicates that the traditional NES is highly robust to the excitation direction. In addition, the NES exhibits notable damping performance within a wide excitation range, especially at high excitation angles. For relatively low and very high excitation intensities, the performance of the NES is poor. The vibration reduction trend under the coupling effect of the excitation intensity and direction is systematically revealed. A critical excitation intensity is identified, at which the NES exhibits weaker performance at low angles but enhanced performance at high angles. The findings provide a theoretical basis for promoting NES engineering applications.