Stretchable and wearable electronics and devices have brought unprecedented opportunities for many applications including robotics, biomedicine, and artificial intelligence. The fundamental materials that enable such applications generally involve soft conductors that combine conductive nanofillers with soft matrices. However, most current soft conductors rely on conventional soft elastomers such as silicone rubber and polyurethane, which are produced from petrochemicals with limited sustainability. In this study, we developed a series of soft nanocomposites based on the integration of sustainable biobased thermoplastic elastomer polystyrene-b-polyfarnesene-b-polystyrene (SFS) with 2D/1D/0D carbon nanofillers. Importantly, SFS and its nanocomposites are fully compatible with extrusion-based 3D printing. We demonstrated pellet 3D-printing of SFS nanocomposites into functional and customizable 3D structures. The mechanical and electrical properties as well as dynamic responses to mechanical deformation of SFS nanocomposites were systematically investigated for their promising applications in wearable sensors and environment monitoring. We found the type/geometry of carbon nanofillers, the ratio between different types of nanofillers, as well as processing conditions (3D printing vs casting) have significant effects on the electrical properties and strain sensor performance. Such 3D printable soft and sustainable nanocomposites provide a new material platform for applications in soft electronics/robotics and human-machine interfaces.