I've noticed you are asking how to develop a wide variety of systems. I would just like to give you a heads up that this is not the place to ask people to do the work for you, especially if you are being paid to implement these solutions.
On the other hand, this sort of thing depends on whether we are talking about an Email client (SMTP/POP) or whether it is a private messaging system within a single website. If it is an SMTP/POP, full on email client then you are looking at programming languages like C++ or various of as well as a good understanding of the protocols required.
If it is a website based system then you would need a server side such as PHP/ASP as well as a database system to store it such as MySQL(i).
Show us what you've got then we can help you, don't just ask for a complete system such as this... especially considering the scale of what you are asking for.