NiTi porous materials with unprecedented superelasticity and shape memory were manufactured by self-entangling, compacting and heat treating NiTi wires. The versatile processing route used here allows to produce entanglements of either superelastic or ferroelastic wires with tunable mesostructures. Three dimensional (3D) X-ray microtomography shows that the entanglement mesostructure is homogeneous and isotropic. The thermomechanical compressive behavior of the entanglements was studied using optical measurements of the local strain field. At all relative densities investigated here ($\sim$ 25 - 40$\%$), entanglements with superelastic wires exhibit remarkable macroscale superelasticity, even after compressions up to 25$\%$, large damping capacity, discrete memory effect and weak strain-rate and temperature dependencies. Entanglements with ferroelastic wires resemble standard elastoplastic fibrous systems with pronounced residual strain after unloading. However, a full recovery is obtained by heating the samples, demonstrating a large shape memory effect at least up to 16% strain.