After reviewing several websites with their take on the difference between these 2 words, I think: "To be obliged" means: - to be in someone’s debt because they did you a favour or service. Example: "As your best friend, I am obliged to tell you the truth. That guy is a jerk!" (here, I am sort of in your debt because you've been such a good friend to me) "To oblige someone" means to place that person under a debt of gratitude by doing a favour or service. Examples: "He will oblige us with a song." (here, since he is doing something nice for us, we are in his debt and should be grateful) "To be obligated" means to be forced by law or morality (the morality part is debatable. Most people associate "oblige" with morality instead). Example: "He is obligated (by law) to inform his neighbours that he's a registered sex offender." However, it seems that British English has done away with "obligate" and is using "obliged" to represent all those definitions, even the ones that involve the law. The frequency of the usage of these two words also depends on location/culture. But generally, most people feel that "obligate" has a more severe tone than "oblige", and usually use "obligate" in matters involving law, and "oblige" in matters involving favours or gratitude.

Search for "difference oblige obligate". You'll see plenty of discussions which explain the difference.