Integrated sensing and communication (ISAC) is one of the key usage scenarios for future sixth-generation (6G) mobile communication networks, where communication and sensing (C&S) services are simultaneously provided through shared wireless spectrum, signal processing modules, hardware, and network infrastructure. Such an integration is strengthened by the technology trends in 6G, such as denser network nodes, larger antenna arrays, wider bandwidths, higher frequency bands, and more efficient utilization of spectrum and hardware resources, which incentivize and empower enhanced sensing capabilities. As the dominant waveform used in contemporary communication systems, orthogonal frequency division multiplexing (OFDM) is still expected to be a very competitive technology for 6G, rendering it necessary to thoroughly investigate the potential and challenges of OFDM ISAC. Thus, this paper aims to provide a comprehensive tutorial overview of ISAC systems enabled by large-scale multi-input multi-output (MIMO) and OFDM technologies and to discuss their fundamental principles, advantages, and enabling signal processing methods. To this end, a unified MIMO-OFDM ISAC system model is first introduced, followed by four frameworks for estimating parameters across the spatial, delay, and Doppler domains, including parallel one-domain, sequential one-domain, joint two-domain, and joint three-domain parameter estimation. Next, sensing algorithms and performance analyses are presented in detail for far-field scenarios where uniform plane wave (UPW) propagation is valid, followed by their extensions to near-field scenarios where uniform spherical wave (USW) characteristics need to be considered. Finally, this paper points out open challenges and outlines promising avenues for future research on MIMO-OFDM ISAC.