Fiber - a primitive yet ubiquitous form of material - intertwines with our bodies and surroundings, from constructing our fibrous muscles that enable our movement, to forming fabrics that intimately interface with our skin. In soft robotics and advanced materials science research, actuated fibers are gaining interest as thin, flexible materials that can morph in response to external stimuli. In this paper, we build on fluidic artificial muscles research to develop OmniFiber - a soft, line-based material system for designing movement-based interactions. We devised actuated thin (øouter < 1.8 mm) fluidic fibers with integrated soft sensors that exhibit perceivably strong forces, up to 19 N at 0.5 MPa, and a high speed of linear actuation peaking at 150mm/s. These allow to flexibly weave them into everyday tangible interactions; including on-body haptic devices for embodied learning, synchronized tangible interfaces for remote communication, and robotic crafting for expressivity. The design of such interactive capabilities is supported by OmniFiber's design space, accessible fabrication pipeline, and a fluidic I/O control system to bring omni-functional fluidic fibers to the HCI toolbox of interactive morphing materials.