In nature, climbing trees and pipes of varying diameters or even navigating inside of hollow pipes and tree holes is easy for some climbing animals and insects. However, today's pipe-climbing robots, which are important for automatically conducting periodic inspections and maintenance of pipelines to save time and keep humans away from hazardous environments, are designed mainly for a specific task, limiting their adaptability to different working scenarios and further implementation in real-life. In this paper, we propose a pipe-climbing robot with a soft linear actuator for bioinspired propulsion, two origami clutches to realize multi-degrees-of-freedom (DoF) motion and two pairs of soft modular legs for multimodal climbing. Design, modeling and experimental validation of the origami clutch are introduced in detail. Preliminary experimental results show that we can achieve a stroke of up to 289.6% and a maximum 45° bending angle on the soft linear actuator by regulating the air pressure inside the soft actuator and origami clutches. Additionally, by choosing the leg-type, three climbing modes, including out-pipe versatile mode, out-pipe high-force mode and in-pipe mode can be realized for particular working scenarios. A prototype climbing robot demonstrates that in out-pipe versatile mode, the robot can climb on the exterior of pipes made of various materials including PVC, rubber and metal with diameters ranging from 105 to 117 mm. In the out-pipe high-force mode, the climber can navigate along a specific pipe carrying maximum 675 g external load at the top or 200 g hanging from the bottom, as well as keeping functional without failure under static loads as high as 1968 g. In the in-pipe mode, the robot is able to travel inside pipes. This research might bridge the design gap between in-pipe and out-pipe climbing robots while offering an alternative option for soft robots to execute multi-DoF motion.