Mode and polarization-division multiplexing technologies (MDM and PDM)can offer considerable parallelism for optical multiplexing biosensors, complex optical neural networks, and high-capacity optical interconnects, while requiring only a single-wavelength laser source. Thanks to the mature fabrication processes of silicon nitride and superior material properties of lithium niobate, the silicon nitride loaded lithium niobate on insulator (LNOI) platform allows the integration of high-speed optical modulators and optical (de)multiplexing devices to achieve high-capacity and low-cost photonic integrated circuits suitable for data communication applications. In this contribution, MDM and PDM are investigated in a silicon nitride loaded LNOI (X-cut) platform. As a proof of concept, an asymmetrical directional coupler-based mode ( de)multiplexer (MMUX) and polarization splitter-rotator (PSR) are designed, fabricated, and experimentally demonstrated. The measured insertion losses are lower than 1.46 and 1.49 dB, while the inter-modal crosstalk is lower than −13.03 and −17.75 dB for the MMUX and PSR, respectively, for a wavelength range of 1525-1565 nm. A 40 Gbps data transmission experiment demonstrates the data transmission capabilities of the fabricated devices. The measured eye diagrams are clear and wide-open, and the bit error rate measurements show reasonable power penalties, indicating good device performance.