You don't have to use inheritance with Java. In fact, in most cases it's better that you don't. Practically all of the Java standard library doesn't require the use of inheritance, same with most modern libraries.

On the contrary, I think inheritance is a very natural way to think. However, that doesn't translate into readable and easy to maintain code in the vast majority of the cases.

I am not sure what you mean by how it's stored or manipulated on a computer. A garbage collected language like Java manages the memory for you. It doesn't really care if your code is using inheritance or not. And unless you're trying to squeeze the last drops of performance out of your code, the memory layout shouldn't be on your mind.