I will not give an exhaustive list explaining the difference or attempt to define the nuances of the boundaries between them (because that is hard and I am sure someone else is better qualified to answer.) What I will do is point out some obvious differences that spring to mind, cases where to use the words interchangeably would just be wrong.

• Prestige is far less broad ranging in meaning than reputation. It refers to a ranking along some scale of generalized impressiveness with which you can demand they be considered.
• Reputation can refer more generally to anything that popular belief attributes to you. This will particularly apply to traits that you can be expected to display. It may be the case that you have a reputation for doing good work and that this work has also given you prestige, but the two don't always go hand in hand. You can have a reputation of not being as prestigious but of being right more often. You can have a reputation for being lousy at securing prestige...
• Status can be influenced by prestige and reputation. With prestige in particular it is hard to get prestige without getting some degree of status. But you can certainly have status without having any prestige whatsoever.
• Status is an approximation of what you would get if you could ask a tribe of social animals to line themselves up in order of dominance, rank or in general awesomeness.

Someone else (or me with more time) could almost certainly provide a clearer picture of the differences but that scratches the surface somewhat.