Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), a fundamental transmission scheme, promises high throughput and robustness against multipath fading. However, these benefits rely on the efficient detection strategy at the receiver and come at the expense of the extra bandwidth consumed by the cyclic prefix (CP). We use the iterative orthogonal approximate message passing (OAMP) algorithm in this paper as the prototype of the detector because of its remarkable potential for interference suppression. However, OAMP is computationally expensive for the matrix inversion per iteration. We replace the matrix inversion with the conjugate gradient (CG) method to reduce the complexity of OAMP. We further unfold the CG-based OAMP algorithm into a network and tune the critical parameters through deep learning (DL) to enhance detection performance. Simulation results and complexity analysis show that the proposed scheme has significant gain over other iterative detection methods and exhibits comparable performance to the state-of-the-art DL-based detector at a reduced computational cost. Furthermore, we design a highly efficient CP-free MIMO-OFDM receiver architecture to remove the CP overhead. This architecture first eliminates the intersymbol interference by buffering the previously recovered data and then detects the signal using the proposed detector. Numerical experiments demonstrate that the designed receiver offers a higher spectral efficiency than traditional receivers. Finally, over-the-air tests verify the effectiveness and robustness of the proposed scheme in realistic environments.