Additive Manufacturing (AM) is a promising solution for handling the complexity of fabricating soft robots. However, the AM of hyperelastic materials is still challenging with limited material types. Within this work, pellet-based 3D printing of very soft thermoplastic elastomers (TPEs) was explored. Our results show that TPEs can have similar engineering stress and maximum strain as Ecoflex OO-10. These TPEs were used to 3D-print airtight thin membranes (0.2-1.2 mm), which could inflate up to a stretch of 1320\%. Combining the membrane's large expansion and softness with the 3D printing of hollow structures simplified the design of a bending actuator that can bend 180 degrees and reach a blocked force of 238 times its weight. In addition, by 3D printing TPE pellets and rigid filaments, the soft membrane could grasp objects by enveloping an object or as a sensorized sucker, which relied on the TPE's softness to conform to the object or act as a seal. In addition, the membrane of the sucker was utilized as a tactile sensor to detect an object before adhesion. These results suggest the feasibility of 3D printing soft robots by using soft TPEs and membranes as an interesting class of materials and sensorized actuators, respectively.