This work presents a novel soft actuator with a 3D-printed elastic body based on a fused-deposition-modeling technique and with tendon actuation based on flexible shafts, which allow push, pull, and twist torque transmissions. The combination of the soft body and flexible shaft furnishes an easy-making, modular and functional unit that possesses softness and enables three degrees of freedom. We derive the kinematics and statics of the actuator based on the assumption of piecewise constant curvature, and identify the parameters experimentally. To understand the performance of the soft actuator in different design and fabrication settings, extensive experiments are performed to compare different shapes of cross sections, infill densities, infill patterns, dentation structures and moment arms in terms of generating forces under the same pulling forces. In addition, experimental validations are performed to characterize other properties such as workspace, hysteresis, pushing force, transmitted torque, and tip force under both bending and twisting. Finally, three potential applications, i.e., a soft robotic hand, a multisegment continuum robot, and a miniaturized drilling device, are prototyped and presented experimentally where the flexibility endowed by the shafts is demonstrated and highlighted. The scalability and modularity are also showcased in the three applications.