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In this paper, we explore a dual-functional radar-communication (DFRC) system for achieving integrated sensing and communications (ISAC). The technique of orthogonal frequency division multiplexing (OFDM) is leveraged to overcome the frequency-selective fading of the wideband multiple-input multiple-output (MIMO) systems with one multi-antenna DFRC base station (BS) and multiple single-antenna user equipment (UEs). In order to restrain the high peak-to-average power ratio (PAPR) of OFDM signals, we aim to jointly design low-PAPR DFRC MIMO-OFDM waveforms. This is done by utilizing a weighted objective function on both communication and radar performance metrics under power and PAPR constraints. The formulated optimization problems can be equivalently transformed into standard semi-definite programming (SDP) and can be effectively solved by semi-definite relaxation (SDR) method, where we prove that globally optimal rank-1 solution can be obtained in general. We further develop a low-complexity method to solve the problems with much reduced overheads. Moreover, the practical scenario with oversampling on OFDM signals is further considered, which has a significant effect on the resulting PAPR levels. The feasibility, effectiveness, and flexibility of the proposed low- PAPR DFRC MIMO-OFDM waveform design methods are demonstrated by a range of simulations on communication sum rate, symbol error rate as well as radar beampattern and detection probability.