Is there any relation to memory optimization when we call a method by using an interface. Is only that method loaded in memory? When a invoke a method via an object are all the methods of that object loaded into memory?
Interface based programming does not relate to memory consumption - it is a technique to increase separation of concerns.
When you use an interface as a parameter (for example), you will still need to pass in an actual object that implements that interface. You will be accessing it via the interface and you could replace it with any other object that implements the interface. This is how you create a decoupled method. You still need memory for the actual object passed in.
It doesn't matter if you call a method via an interface or via a reference to the object. An interface reference still references an instance. The type has a number of methods and these are loaded as the type is loaded (and JIT compiled as needed).
No, there is no practical difference between calling a method using an interface and calling it using a class.
When you use an interface, it's just your reference that is different. The reference still points to an instance of a class. There can't be an instance of an interface as the interface itself doesn't contain any implementation, so there is always an instance of a class in the other end.
What methods are loaded into memory has nothing to do with interfaces. In .NET, when a method is first called, it is compiled into native code, which is then kept in the memory. It doesn't matter how are you accessing it (whether directly, through interface, or using a delegate).
Also, memory consumption by methods themselves should be really low and nothing you should care about.
Slightly vague question. I'm guessing you are asking if using interfaces incur performance penalties in whatever language you're using.
The answer is generally.. for C++ (pure virtual functions), yes. Can be significant in certain very-many-calls situations.
For Java (and .Net probably), not really.
See: http://stackoverflow.com/questions/890687/overhead-of-implementing-an-interface