Nice to hear that you progressed.
In MPI parallel mode the OOFEM relies on external libraries like PETSc to solve the distributed sparse linear system in parallel. It will not work with non-MPI linear solvers, as the governing equation contributions (LHS, RHS, etc) are assembled and stored on individual processing nodes.
The shared memory model will work also without OpenMP aware solver, but only the system assembly will run in parallel. If combined with OpenMP enabled solver, such as Pardiso or Super-LU, one will get also the solution of linear system in parallel.
The hybrid approach is also possible, combining MPI based approach (coarse grain decomposition) with OpenMP processing on individual nodes, but efficient utilization of resources need to be supported by the linear equation solver.
The actual approach depends on use case, particularly on the problem size. OpenMP can scale reasonably to 16-20 CPUs, then due to the limitations of the HW architecture the scaling is lost. MPI offers much better scalability in general and is suitable for large problems.