This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Ahem! You have casually asked a few major questions in one go!
To quickly answer your questions:
RMI is about communication between objects residing in different JVMs where the JVMs can be located in different machines too i.e. it is a distributed environment. You can invoke methods on an object residing in another JVM using RMI. RMI uses socket programming behind the scenes to achieve this i.e. the developer need not worry about the n/w programming details when s/he codes to achieve RMI.
A servlet is a Java class used to extend the capabilities of a server where the server hosts applications and allows them to be accessed using a request-response type of approach. A servlet is mostly used in web applications where the client and the server communicate using the HTTP protocol. The order of communication of the HTTP request will be client -> web server -> web container -> servlet. Every HTTP servlet has a life cycle of its own.
If possible, buy yourself a copy of the Head First series of books.