By harnessing the delay-Doppler (DD) resource domain, orthogonal time-frequency space (OTFS) substantially improves the communication performance under high-mobility scenarios by maintaining quasi-time-invariant channel characteristics. However, conventional multiple access (MA) techniques fail to efficiently support OTFS in the face of diverse communication requirements. Recently, multi-dimensional MA (MDMA) has emerged as a flexible channel access technique by elastically exploiting multi-domain resources for tailored service provision. Therefore, we conceive an elastic multi-domain resource utilization mechanism for a novel multi-user OTFS-MDMA system by leveraging user-specific channel characteristics across the DD, power, and spatial resource domains. Specifically, we divide all DD resource bins into separate subregions called DD resource slots (RSs), each of which supports a fraction of users, thus reducing the multi-user interference. Then, the most suitable MA, including orthogonal, non-orthogonal, or spatial division MA (OMA/ NOMA/ SDMA), will be selected with each RS based on the interference levels in the power and spatial domains, thus enhancing the spectrum efficiency. Then, we jointly optimize the user assignment, access scheme selection, and power allocation in all DD RSs to maximize the weighted sum-rate subject to their minimum rate and various practical constraints. Since this results in a non-convex problem, we develop a dynamic programming and monotonic optimization (DPMO) method to find the globally optimal solution in the special case of disregarding rate constraints. Subsequently, we apply a low-complexity algorithm to find sub-optimal solutions in general cases.