I think "impediment" and "hindrance" are synonyms, and "obstacle" is almost a synonym. To me, "obstacle" suggests something that actually stops you while "impediment" and "hindrance" only slow you down. "Impediment" is often heard in the phrase "speech impediment," conditions interfering with speech, such as a stutter (Trouble de la parole, Bégaiement). "Impediment" is not common in other contexts. I wonder if by any chance you've been reading the famous sonnet of Shakespeare that begins "Let me not to the marriage of true minds Admit impediments. Love is not love Which alters when it alteration finds, Or bends with the remover to remove." That's old-fashioned language--and hard for native English-speakers to understand!