Since the emergence of monolayer graphene as a promising two-dimensional material, many other monolayer and few-layer materials have been investigated extensively. An experimental study of few-layer Si2Te3 was recently reported, showing that the material has diverse properties for potential applications in Si-based devices ranging from fully integrated thermoelectrics to optoelectronics to chemical sensors. This material has a unique layered structure: it has a hexagonal closed-packed Te sublattice, with Si dimers occupying octahedral intercalation sites. Here we report a theoretical study of this material in both bulk and monolayer form, unveiling a fascinating array of diverse properties arising from reorientations of the silicon dimers between planes of Te atoms. The lattice constant varies up to 5% and the band gap varies up to 40% depending on dimer orientations. The monolayer band gap is 0.4 eV larger than the bulk-phase value for the lowest-energy configuration of Si dimers. These properties are, in principle, controllable by temperature and strain, making Si2T3 a promising candidate material for nanoscale mechanical, optical, and memristive devices.