Epilog doesn't have options in the sense that Plot, Style and other functions have options. It allows you to add (actually, overlay, I think) additional graphic elements onto a Plot, ListPlot, etc.  The graphic elements you add have options themselves, however.  For example, Mathematica's documentation for Epilog shows the following example:

If you look in the documentation for Point, you find that it has its own options and properties, and works in its own particular way:

The same will be true for all the functions you use with Epilog.  You can use Epilog to add a list of graphic elements (Epilog->{expression1, expression2, ...}), each of which can be a function with its own options, so it's really about the expressions you use Epilog to add.  I hope this is helpful, and I haven't made the annoying assumption that you know less than you really do.