Spin defects in diamond serve as powerful building blocks for quantum technologies, especially for applications in quantum sensing and quantum networking. Electron-nuclear defects formed in the environment of optically active spins, such as the nitrogen-vacancy (NV) center, provide a resource for multi-qubit quantum registers. However, many of these defects have yet to be characterized, limiting their control and integration in quantum devices. Here, we apply two hybrid electron-nuclear spin control schemes to self-consistently characterize unknown spin defects at the single-spin level. We perform double electron-electron resonance at zero field (ZF-DEER) to extract hyperfine components and introduce a nuclear-electron-electron triple resonance (NEETR) protocol to control and identify the nuclear spin through the stronger electronic spin interaction. These results provide a guide to resolving the defect structures using ab initio calculations, leading to the identification of a new hydrogen-related defect structure as well as an accurate match to a previously identified nitrogen-related defect. We further apply our NEETR protocol to demonstrate initialization, unitary control, and long-lived coherence of the hydrogen nuclear spin qubit with = 1.0(3)\,\mathrm{ms}$. Together, these characterization and control tools establish a framework to harness previously unknown electron-nuclear defects for quantum register applications.