The exceptional thermal conductivity and strength of carbon nanotubes (CNTs) position them as outstanding materials for thermal conduction. The intriguing properties introduced by van der Waals (vdW) heterojunctions have also captured the interest of researchers. However, further refinement of the research concerning the integration of these two elements is required. In our study, a vdW heterostructure with asymmetric layer nesting of multiwalled CNTs (ALCNTs) is devised, with a specific focus on the model's heat flux and thermal rectification (TR) properties, which are analyzed using nonequilibrium molecular dynamics (NEMD). Notably, the greatest TR ratio is observed in the connection of three-layer and single-layer ALCNTs. Moreover, multilayer variable-length nested models exhibit a sluggish TR ratio. An examination of the interface thermal resistance (ITR) reveals that the maximum ITR in the multilayer nested model resides at the rightmost interface. However, it is essential to highlight that the determinant of the TR ratio and heat flux in the multilayer nested model is not the maximum ITR of the rightmost interface but rather the ITR of the outermost layer on the left. Additionally, the impacts of the defect density, length, temperature difference, and hydrogenation on the model's heat flux and TR are explored, yielding noteworthy conclusions. For instance, defects in the outer CNT have a minimal influence on the heat flux and TR compared with those in the inner CNT. As the length increases, the heat flux initially decreases and then increases. Hydrogenation significantly enhances the model's heat flux but does not favor the TR. Our study contributes to advancing the understanding of CNT vdW heterojunctions and offers valuable insights for their practical applications.