The rapid progress in 6G communication and high-bandwidth radar has driven an unprecedented surge in the spatial density of signal sources, resulting in an increasingly congested electromagnetic (EM) environment. When resolving closely spaced signals and interference, existing architectures are strictly bounded by the inherent diffraction limits of two-dimensional (2D) physical apertures, hindering super-resolution sensing and multi-interference mitigation in complex scenarios. Here, we present a 3D aperture-engineered diffractive neural network (AE-DNN) that achieves super-resolution sensing and computing by extending the traditional 2D aperture into 3D. The 3D aperture engineering framework is realized by constructing deep cascaded metasurface layers so that the diffractive propagation from oblique incident fields can be layer-wise modulated and piecewise encoded for perceiving EM fields far exceeding physical aperture limits. The N-layer AE-DNN has the capability to achieve ~N times higher angular resolution than the 2D aperture diffraction limit. The multi-dimensional synthetic aperture (MSA) training is developed to achieve speed-of-light coherent synthesis of the 3D aperture and integrate neural network-based modeling of multi-dimensional metasurface modulation. By orthogonalizing array response vectors in the analog domain, AE-DNN performs parallel super-resolution angle estimation, source number estimation, and source separation for up to 10 independent coherent or incoherent sources. Experimental results across the 36-41 GHz band demonstrate that AE-DNN resolves and suppresses closely spaced multi-interference by ~20 dB, enhances communication capacity by 13.5X, and reduces latency by three orders of magnitude. AE-DNN heralds a paradigm shift in signal processing for advanced radar and 6G communications.