The recent discovery and realizations of higher-order topological insulators enrich the fundamental stud-ies on topological phases.Here,we report three-dimensional(3D)wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topol-ogy originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide sym-metry of the lattice.The multitude of topological states brings diverse possibilities of wave manipulations.Through judicious engineering of the boundary modes,we experimentally demonstrate two functionalities at different dimensions:2D negative refraction of sound wave enabled by a first-order topological surface state with negative dispersion,and a 3D acoustic interferometer leveraging on second-order topological hinge states.Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.