Your request is somewhat ambiguous, and you may be thinking it's more complex than it is.
I've attached an example that makes no use at all of AND, OR, NOT... It's possible to use start and end dates and three different rules within a single conditional format collection, to color different dates differently depending on where they are in relationship to those start and end dates. I've attached the actual spreadsheet, but here's a screen grab that shows the Conditional Formatting dialog window, as well as the sheet itself, with start and end dates two months apart, and a series of dates to each of which all three rules apply, but with different consequences.
