Several experimental detections have demonstrated the existence of Borromean states predicted by Vitaly Efimov within a nuclear physics context, that is, trimers bound despite the absence of bound states of any of the two-body subsystems. I show that novel Efimov Physics is expected in gravitationally polarizable nonbaryonic dark matter beyond the Standard Model with van der Waals-like forces driven by quantum gravitational fluctuations. I also discuss ground and space-based tests of spacetime curvature effects on weakly bound, highly diffuse quantum three-body systems with standard electrodynamical van der Waals forces. Finally, I consider exotic gravitational quantum matter from higher-order Brunnian structures and analogies with classical systems, already proven in three-stranded DNA, driven by the stochastic gravitational wave background.