Installing ODT and ODAC ?

     source : https://community.oracle.com/thread/483439

ODAC will be required by all clients that uses Oracle Data Provider for .NET to access Oracle Database. ODAC installation includes Oracle Client, so you don't need to install Oracle Client separately because ODAC already does it for you.

Are the "Oracle Development tools" and "Oracle Extensions for .Net" the same thing?

"Oracle Development tools" (or ODT) is a tool to access oracle directly from VS.NET IDE
"Oracle Extensions for .Net" (or ODE) is an extension to enable you code stored procedure using .NET languages.

Do I install them on the server or the client

install ODT only on development machine which usually has VS.NET installed.
install ODE only on server machine to enable developer deploys their .NET stored procedures
install ODAC (which includes Oracle Client) on all client computers which need access to oracle database, you don't need to install ODAC on database server.