There may not be a right answer but hopefully there can be a best answer. Obviously we use these terms quite interchangeably (which I find annoying), and dictionaries have a lot of overlap in their definitions of these words because dictionaries often don't attempt to contrast words with each other. But if we had to give some rigorous definitions to these words what would they be? They can still have overlap, as long as the overlap is clearly explained. I prefer answers that prove themselves with examples of how your definitions already match with popular usage.
These words (can) all share the same meaning of describing what something is like or what it has. But then what are their useful differences? Some details to consider: which of these are more abstract and which are more tangible? which are more tightly bound to an object and which are more alienable? which are more subjective and which are more objective?
Here is some pre-research for you. (Or a source of confusion.) Pertinent definitions from dicionary.com.
property a quality, attribute, or distinctive feature of anything, esp a characteristic attribute such as the density or strength of a material
quality an essential or distinctive characteristic, property, or attribute: the chemical qualities of alcohol.
characteristic a distinguishing feature or quality: Generosity is his chief characteristic.
attribute something attributed as belonging to a person, thing, group, etc.; a quality, character, characteristic, or property: Sensitivity is one of his attributes.
feature a prominent or conspicuous part or characteristic: Tall buildings were a new feature on the skyline.
trait a distinguishing characteristic or quality, especially of one's personal nature: bad traits of character.
aspect nature; quality; character: the superficial aspect of the situation.