We investigate the topological classification and properties of nonabelian vortices that arise in a 2-dimensional film of a two-component condensate. For a repulsive interaction between the condensates, we realize an order parameter in the ordered configuration space of three complex numbers C₃(C). Analyzing the homotopic properties, we find the emergence of elementary nonabelian vortex-antivortex pairs connected by energetic strings that are rooted in the repulsive interaction and carry the nonabelian information. Moreover, we predict the existence of Brunnian vortices, which are textures exhibiting zero net winding of the condensate phases and can only be detected by a higher-order winding number. Finally, to motivate technological applications rooted in nonabelian vortex transport, we devise a nonvolatile memory storage device that encodes topologically robust information.