Nuclear quadrupolar resonance (NQR) spectroscopy reveals chemical bonding patterns in materials and molecules through the unique coupling between nuclear spins and local fields. However, traditional NQR techniques require macroscopic ensembles of nuclei to yield a detectable signal, which obscures molecule-to-molecule variations. Solid-state spin qubits, such as the nitrogen-vacancy (NV) center in diamond, facilitate the detection and control of individual nuclei through their local magnetic couplings. Here, we use NV centers to perform NQR spectroscopy on their associated nitrogen-14 (¹⁴N) nuclei at room temperature. In mapping the nuclear quadrupolar Hamiltonian, we resolve minute variations between individual nuclei. The measurements reveal correlations between the Hamiltonian parameters associated with the NV center’s electronic and nuclear spin states, as well as a previously unreported symmetry-breaking quadrupolar term. We further design pulse sequences to initialize, read out, and control the quantum evolution of the ¹⁴N nuclear state using the nuclear quadrupolar Hamiltonian.