The transition from isolated systems to integrated solutions has driven the development of space-air-ground integrated networks (SAGIN) as well as the integration of communication and radar sensing functionalities. By leveraging the unique properties of the Terahertz (THz) band, THz joint communication and radar sensing (JCRS) supports high-speed communication and precise sensing, addressing the growing demands of SAGIN for connectivity and environmental awareness. However, most existing THz studies focus on terrestrial and static scenarios, with limited consideration for the dynamic and non-terrestrial environments of SAGIN. In this paper, the THz JCRS techniques for SAGIN are comprehensively investigated. Specifically, propagation characteristics and channel models of THz waves in non-terrestrial environments are analyzed. A link capacity comparison with millimeter-wave, THz, and free-space optical frequency bands is conducted to highlight the advantages of THz frequencies. Moreover, novel JCRS waveform design strategies are presented to achieve mutual merit of communication and radar sensing, while networking strategies are developed to overcome challenges in SAGIN such as high mobility. Furthermore, advancements in THz device technologies, including antennas and amplifiers, are reviewed to assess their roles in enabling practical JCRS implementations.