Constructing van der Waals (vdW) heterostructures is a prospective approach that is essential for developing a new generation of functional two-dimensional (2D) materials and designing new conceptual nanodevices. Using density-functional theory combined with a nonequilibrium Green's function approach allows for the theoretical and systematic exploration of the electronic structure, transport properties, and sensitivity of organic small molecules adsorbed on 2D C3B/graphene (Gra) and C3N/Gra vdW heterojunctions. Calculations show the metallic properties of C3B/Gra and C3N/Gra after the formation of heterojunctions. Interestingly, the heterojunctions C3B/Gra (C3N/Gra) for the adsorption of small organic molecules (C2H2, C2H4, CH3OH, CH4, and HCHO) at the C3B (C3N) side are sensitive to the chemisorption of C2H2 and C2H4. Similarly, the Gra/C3B is chemisorbed for both C2H2 and C2H4 when adsorbed on Gra side, while it is only chemisorbed for C2H2 in Gra/C3N. Interestingly, all heterojunctions on different sides are physisorbed for CH3OH, CH4, and HCHO. Furthermore, the calculated I-V curves demonstrate that the devices based on the adsorption of C2H2 and C2H4 at each side of the heterojunction have remarkable anisotropy, in with the current being considerably greater in the zigzag direction than in the armchair direction. More specifically, with C2H2 adsorbed on the Gra side, the sensitivity along the armchair direction is up to 85.0% for Gra/C3B and close to 100% for Gra/C3N. This study reveals that C3B/Gra (C3N/Gra) heterojunctions with high selectivity, high anisotropy, and excellent sensitivity are highly prospective 2D materials for applications, which further contributes new insights into the development of future electronic nanodevices.