Colliding winds in massive binaries generate X-ray-bright shocks, synchrotron radio emission, and sometimes even dusty "pinwheel" spirals. We report the first X-ray detections of the dusty WC+O binary system WR 112 from Chandra and Swift, alongside 27yr of Very Large Array/Australia Telescope Compact Array radio monitoring and new diffraction-limited Keck images. Because we view the nearly circular orbit almost edge-on, the colliding-wind zone alternates between heavy Wolf-Rayet wind self-absorption and near-transparent O-star wind foreground each 20yr orbit, producing phase-locked radio and X-ray variability. This scenario leads to a prediction that the radio spectral index is flatter from a larger nonthermal contribution around the radio intensity maximum, which indeed was observed. Existing models that assume a single dust-expansion speed fail to reproduce the combined infrared (IR) geometry and radio light curve. Instead, we require an accelerating postshock flow that climbs from near-stationary to ~1350km/s in about one orbital cycle, naturally matching the IR spiral from 5" down to within 0.1", while also fitting the phase of the radio brightening. These kinematic constraints supply critical boundary conditions for future hydrodynamic simulations, which can link hot-plasma cooling, nonthermal radio emission, X-ray spectra, and dust formation in a self-consistent framework. WR 112 thus joins WR 140, WR 104, and WR 70-16 (Apep) as a benchmark system for testing colliding-wind physics under an increasingly diverse range of orbital architectures and physical conditions.