what are the various parallel port interface supported by NIOSII?

Your question is a bit difficult to answer because it's slightly incorrect. A processor (such as NIOSII) does not support a parallel port interface. Processors have physical address and data buses which are used to access external memory or peripherals. A microcontroller on the other hand typically includes specific peripheral interfaces.

The NIOS is a soft-core processor. In theory it supports any peripheral in the world. You just have to connect that peripheral to the NIOS's data bus for the peripheral to be accessible.

Anyway now to answer your question more specifically. For parallel I/O, a lot of people typically use the PIO core peripheral. You can connect as many of these to the processor as you like (hundreds even). Then you just have to write the software on the other end to control the port(s) as you would like.

An experienced NIOS designer could create the system you desire in a manner of minutes. So what you are trying to do is entirely possible. Here is where you should be looking to increase your understanding:

http://www.altera.com/literature/lit-nio2.jsp

Look under "Volume 5: Embedded Peripherals"

Jake