WPA and WPA2 are all actually interim protocols that are used until the standardization of IEEE 802.11i standard. Wi-fi appliance decided that ratification and standardization of 802.11i standards will take more time. So, they came up with WPA.
Now, WPA2 is advanced version of WPA. WPA2 uses AES as encryption algorithm. Whereas, WPA use TKIP as encryption mode which in turn uses RC4 encryption algorithm.
WPA and WPA2 are actually are of 2 types respectively.
WPA/WPA2-PSK - This is mainly for small offices. This uses Pre-Shared Key for authentication.
WPA/WPA2 -Enterprise - This uses a RADIUS Server for authentication. This is an extension to 802.1x authentication. But this uses stronger encryption scheme(WPA uses RC4 and WPA2 uses AES).
Any authentication mechanism that involves a separation authentication server for authentication like ACS server is called 802.1x authentication.
EAP stands for Extensible Authentication Protocol. It refers to the type or method of 802.1x Authentication by the RADIUS/Tacacs server. A RADIUS server can authenticate a wireless client with various EAP methods.
LEAP is one type of EAP. It uses username and password for authenticating wireless clients. LEAP is cisco proprietory.
There are also EAP types which uses other user credentials like Certificates, SIM etc for authentcation.