Liquid crystals ordering of DNA and RNA oligomers relies on the presence of inter-duplex end-to-end attraction, driving the formation of linear aggregates. Such interactions are gauged, at a macroscopic level, by the osmotic pressure at the isotropic-nematic and nematic-columnar phase transitions. We studied aqueous solutions of PEG and DNA duplex-forming oligomers, finding that there is a wide range of concentrations in which these mixtures phase separate into coexisting PEG-rich and DNA-rich phases, the latter being either in the isotropic state or ordered as a nematic or columnar liquid crystal. We determined the phase diagram in mixtures of PEG and DNA duplexes with different terminal motifsblunt ends, sticky overhangs, aggregation-preventing overhangsand measured the partitioning of the species in the coexisting phases. On this basis, we determined the osmotic pressure as a function of the DNA concentration across the phase diagram. We compared the equation of state obtained in this way with both the Carnahan-Starling equation of state for hard spheres and with the pressure predicted by computer simulations of a system of aggregating cylinders. We obtain a good agreement between experiments and simulations, and end-to-end attraction energies of the order of 6 kcal/mol, a bit larger than expected, but still in agreement with the current models for DNA-DNA interactions.