Compared to artificial metamaterials, where nano-fabrication complexities and finite-size inclusions can hamper the desired electromagnetic response, several natural materials like van der Waals crystals hold great promise for designing efficient nanophotonic devices in the optical range. Here, we investigate the unusual optical response of NiTe, a van der Waals crystal and a type-II Dirac semimetal hosting Lorentz-violating Dirac fermions. By {\it ab~initio~} density functional theory modeling, we show that NiTe harbors multiple topological photonic regimes for evanescent waves (such as surface plasmons) across the near-infrared and optical range. By electron energy-loss experiments, we identify surface plasmon resonances near the photonic topological transition points at the epsilon-near-zero (ENZ) frequencies , , and eV. Driven by the extreme crystal anisotropy and the presence of Lorentz-violating Dirac fermions, the experimental evidence of ENZ surface plasmon resonances confirm the non-trivial photonic and electronic topology of NiTe. Our study paves the way for realizing devices for light manipulation at the deep-subwavelength scales based on electronic and photonic topological physics for nanophotonics, optoelectronics, imaging, and biosensing applications.