I have an idea about the basics, but I'm fuzzy on the details, and it's been awhile since I've studied the subject in depth. Anyone have some answers?
恩 - favor or kindness from others that one should be feeling a sense of gratitude toward
義務 - duty rooted in social systems, usually associated with legal senses, such as liability or military service
義理 - duty rooted in personal relations usually friendship. family relations never or rarely come in this category.
人情 - pity or sympathy one feels when facing someone else's undeserved accident/accusation
義理がある/ない - describes a person or people or their relation's being or not being observing such duties
かれは義理がある He is a faithful person.
かれは義理がない He is a unreliable person.
人情がある/ない - similar to 義理, describing subject's property.
かれは人情がある He is easily moved by compassion.
かれは人情がない He is cold-hearted.
義務がある/ない - describes such duties' being put on or waived from someone or a group
かれは兵役の義務がある He has to serve his country.
かれは兵役の義務がない He is exempted from military service.
not a valid expression see comments