Hybrid nanoparticles with multiple functions are of great interest in biomedical diagnostics, therapies, and theranostics but typically require complex multistep chemical synthesis. Here we demonstrate a general physical method to create multifunctional hybrid materials through aerosol-phase graphene encapsulation of ensembles of simple unifunctional nanoparticles. We first develop a general theory of the aerosol encapsulation process based on colloidal interactions within drying microdroplets. We demonstrate that a wide range of cargo particle types can be encapsulated, and that high pH is a favorable operating regime that promotes colloidal stability and limits nanoparticle dissolution. The cargo-filled graphene nanosacks are then shown to be open structures that rapidly release soluble salt cargoes when reintroduced into water, but can be partially sealed by addition of a polymeric filler to achieve slow release profiles of interest in controlled release or theranostic applications. Finally, we demonstrate an example of multifunctional material by fabricating graphene/Au/Fe₃O₄ hybrids that are magnetically responsive and show excellent contrast enhancement as multimodal bioimaging probes in both magnetic resonance imaging and X-ray computed tomography in full-scale clinical instruments.