What is the difference in usage between 以后 and 之后？
之后 means after that (something said earlier) which requires a context as the reference point of time. 以后 can be used with or without context. When standalone, 以后 means from now on, in future. 
In general, 之后 refers to a shorter time period than 以后. The difference is akin to that between after vs. since but weaker. In imperative sentences you may want to use 以后.
之后 can also mean geographically behind though this usage is not common. 以后 cannot be used in that way. Example: 围墙之后是一排小树。 
In colloquial language they are pretty much interchangeable. People don't pay much attention to the differences in #1 and #2. In other word, 之后 can also be used without a context and means from now on, etc. In writing and formal speech, however, they should be used with precision.