Warm, large exoplanets with 10-100 day orbital periods pose a major challenge to our understanding of how planetary systems form and evolve. Although high eccentricity tidal migration has been invoked to explain their proximity to their host stars, a handful reside in or near orbital resonance with nearby planets, suggesting a gentler history of in situ formation or disk migration. Precise characterization of their masses and radii, orbital properties, and resonant behavior can test theories for the origins of planets orbiting close to their stars. Previous characterization of the TOI-216 system using the first six sectors of TESS data suffered from a degeneracy between planet mass and orbital eccentricity. Radial-velocity measurements using HARPS, FEROS, and the Planet Finder Spectrograph break that degeneracy, and an expanded transit timing variations baseline from TESS and an ongoing ground-based transit observing campaign increase the precision of the mass and eccentricity measurements. We determine that TOI-216c is a warm Jupiter, TOI-216b is an eccentric warm Neptune, and that they librate in 2:1 resonance with a moderate libration amplitude, a small but significant free eccentricity, and a small but significant mutual inclination. The libration amplitude, free eccentricity, and mutual inclination imply a disturbance of TOI-216b before or after resonance capture, perhaps by an undetected third planet. We discuss the implications for the origins of warm, large exoplanets.