Surface decoration of nanohydrogels with functional molecules as well as nanomaterials offers a facile approach for developing multifunctional drug nanocarriers. Herein, the surface-tailorable polymer nanohydrogels, with the catechol groups as a universal anchor, were prepared by simple reflux-precipitation polymerization for versatile functionalization as drug delivery systems. The resultant polymer nanohydrogels were not only capable of delivering doxorubicin (DOX) through electrostatic interactions, but also exhibited facile conjugation with magnetic Fe3O4 nanoparticles and anticancer drug bortezomib (BTZ) via the versatile catechol-based coupling chemistry. The DOX and Fe3O4 loaded nanohydrogels (DOX-Fe3O4@NG) exhibited high DOX loading capability and triggered drug release behaviors in the acidic and redox environment. Furthermore, the DOX-Fe3O4@NG achieved improved cellular uptake in the presence of external magnetic field due to the active magnetic targeting properties. As for the dual drug delivery system (DOX-BTZ@NG), the DOX-BTZ@NG also released the drugs in response to the external stimuli including low pH and GSH presence, indicating their intelligent drug delivery properties. In particular, the DOX-BTZ@NG showed higher antiproliferation efficacy to cancer cells in comparison with the single drug loaded nanohydrogels, suggesting a synergistic effect of the dual drug combination therapy. The degradable poly(AA-co-DMA) nanohydrogels with surface-tailorable functionalities are thus a promising versatile platform for conjugation with both nanomaterials and drug molecules.