Inter-carrier interference (ICI) poses a significant challenge for OFDM joint radar-communications (JRC) systems in high-mobility scenarios. In this paper, we propose a novel ICI-aware sensing algorithm for MIMO-OFDM JRC systems to detect the presence of multiple targets and estimate their delay-Doppler-angle parameters. First, leveraging the observation that spatial covariance matrix is independent of target delays and Dopplers, we perform angle estimation via the MUSIC algorithm. For each estimated angle, we next formulate the radar delay-Doppler estimation as a joint carrier frequency offset (CFO) and channel estimation problem via an APES (amplitude and phase estimation) spatial filtering approach by transforming the delay-Doppler parameterized radar channel into an unstructured form. To account for the presence of multiple targets at a given angle, we devise an iterative interference cancellation based orthogonal matching pursuit (OMP) procedure, where at each iteration the generalized likelihood ratio test (GLRT) detector is employed to form decision statistics, providing as by-products the maximum likelihood estimates (MLEs) of radar channels and CFOs. In the final step, target detection is performed in delay-Doppler domain using target-specific, ICI-decontaminated channel estimates over time and frequency, where CFO estimates are utilized to resolve Doppler ambiguities, thereby turning ICI from foe to friend. The proposed algorithm can further exploit the ICI effect to introduce an additional dimension (namely, CFO) for target resolvability, which enables resolving targets located at the same delay-Doppler-angle cell. Simulation results illustrate the ICI exploitation capability of the proposed approach and showcase its superior detection and estimation performance in high-mobility scenarios over conventional methods.