Disclosed herein are polymer-coated iron oxide magnetic nanoparticles and methods of their manufacture and use. The nanoparticles are coated with a copolymer of poly(maleic anhydride alt-H2C═CH—R1)-polyethylene glycol (PMAR-PEG), wherein R1 is a hydrophobic moiety. The molecular weights of the PMAR and PEG portions of the copolymer, as well as the core diameter of the nanoparticles are selected in order to produce optimal performance for specific applications. Representative applications of the nanoparticles include magnetic particle imaging, magnetic sentinel lymph node biopsy, and magnetic fluid hyperthermia. The disclosed nanoparticles are tools for these methods that provide previously unachieved levels of stability (e.g., via reduced agglomeration) and customizability (e.g., tuned blood circulation half-life in vivo).