We present multi-epoch simultaneous radio, optical, H alpha , UV, and X-ray observations of the active, young, low-mass binary NLTT 33370 AB (blended spectral type M7e). This system is remarkable for its extreme levels of magnetic activity: it is the most radio-luminous ultracool dwarf (UCD) known, and here we show that it is also one of the most X-ray luminous UCDs known. We detect the system in all bands and find a complex phenomenology of both flaring and periodic variability. Analysis of the optical light curve reveals the simultaneous presence of two periodicities, 3.7859 + or - 0.0001 and 3.7130 + or - 0.0002 hr. While these differ by only ~2%, studies of differential rotation in the UCD regime suggest that it cannot be responsible for the two signals. The system's radio emission consists of at least three components: rapid 100% polarized flares, bright emission modulating periodically in phase with the optical emission, and an additional periodic component that appears only in the 2013 observational campaign. We interpret the last of these as a gyrosynchrotron feature associated with large-scale magnetic fields and a cool, equatorial plasma torus. However, the persistent rapid flares at all rotational phases imply that small-scale magnetic loops are also present and reconnect nearly continuously. We present a spectral energy distribution of the blended system spanning more than 9 orders of magnitude in wavelength. The significant magnetism present in NLTT 33370 AB will affect its fundamental parameters, with the components' radii and temperatures potentially altered by ~+20% and 10%, respectively. Finally, we suggest spatially resolved observations that could clarify many aspects of this system's nature.