The emergence of dynamic optical switching has opened up new perspectives for lightening the ever growing load on the electrical switches and routers, to meet the increasing demand on high-speed and flexible data processing and management in fiber-optic communications. Despite diversity schemes of optical switching in the single-mode regime, multi-mode switching of the hybrid fiber and chip system enabled by photonic integrated circuits, especially for the fiber-chip-fiber system, is still an outstanding challenge. Here, we propose and demonstrate the mode and polarization transmission and switching fiber-chip-fiber system with few-mode fibers (FMFs), including the FMF links for mode- and polarization-division multiplexing data transmission, the femtosecond (fs)-laser inscribed 3-dimensional (3D) photonic lantern silica chip for (de)multiplexing and coupling between FMFs and chip, and the topology-optimized N × N non-blocking 2-dimensional (2D) silicon switch array chip for switching and routing. Using 30-Gbaud quadrature phase-shift keying signals on wavelength-division multiplexing (WDM) channels, the WDM-compatible hybrid mode/polarization transmission, switching and routing system with FMFs, fs-laser inscribed silica (de)multiplexing chip and silicon switch array chip are demonstrated in the experiment with favorable operation performance. The demonstration may open the door for developing robust multi-dimensional optical data processing in fiber-optic communication systems with versatile fibers and chips.