To my opinion your arsenal of analysis depends a bit of the anion of your IL. Anyhow, you can certainly use multinuclear NMR and LC-MS to characterize your components , at least those coming from ephedrine. In order to study chirality I'd use CD (circular dichroism) spectroscopy by comparing the (sign and shape of the) spectrum of the starting material with that of IL. Probably I'd measure optical rotation as well. Although, I'd never tried for this goal chiral HPLC could also work at appropriate settings.
Your main concerns will be if the chirality was retained and if you have starting material left. Depending on what exactly you do, I would suggest to start with TLC, move over to NMR, shift reagents and NMR to verify chirality and ev. HPLC /Chiral HPLC. You can also try ion chromatography, but it will not give you any info on chirality.