The ability to manipulate nanoscopic matter precisely is critical for the development of active nanosystems. Optical tweezers are excellent tools for transporting particles ranging in size from several micrometres to a few hundred nanometres. Manipulation of dielectric objects with much smaller diameters, however, requires stronger optical confinement and higher intensities than can be provided by these diffraction-limited systems. Here we present an approach to optofluidic transport that overcomes these limitations, using sub-wavelength liquid-core slot waveguides. The technique simultaneously makes use of near-field optical forces to confine matter inside the waveguide and scattering/adsorption forces to transport it. The ability of the slot waveguide to condense the accessible electromagnetic energy to scales as small as 60 nm allows us also to overcome the fundamental diffraction problem. We apply the approach here to the trapping and transport of 75-nm dielectric nanoparticles and lambda-DNA molecules. Because trapping occurs along a line, rather than at a point as with traditional point traps, the method provides the ability to handle extended biomolecules directly. We also carry out a detailed numerical analysis that relates the near-field optical forces to release kinetics. We believe that the architecture demonstrated here will help to bridge the gap between optical manipulation and nanofluidics.