The structure and properties of ionic liquids are subjects of current interest. See, e.g.., Angew. Chem. Int. Ed. 2013, 57, 4623,-4627; Ibid.,2009, 48, 3184-3186.
As far as I know, there is no quantitative information on their effects as "polar", hydrogen bond donors or acceptor solvents. This would allow useful comparisons with more usual solvents, perhaps using solvatochromic parameters. See, e.g. Prog. Phys. Org. Chem. 1981,13, 485-630. This would tie-up with recent important experimental work such as J. Chem. Ing. Data 2012,57, 918-927.