This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
I presume these date's are represented as Strings. If so, parse them to java.util.Date  objects using the (inherited) parse(String) method from the java.text.SimpleDateFormat  class. Now you have three Date objects and you can see if one of them lies in between the other two dates by using Date's before(Date) and after(Date) methods.