I am curious to know which programming model does the ubuntu follows in its own development process; does it follow the object-oriented programming model (and use languages like python, java etc ) or does it follows the traditional procedural programming model (languages like C, ASM).
In general, there is no stipulated language or programming model for Ubuntu.
In Ubuntu, you can use just about any programming language to create your application(s), so long as the language is supported via any bindings and libraries that it requires.
For example, you can write application for Ubuntu that target either GTK+ or Qt, which both support several languages (C++, Python, Java, etc). GTK+ specifically is written in C, but many applications which target GTK+ use Python.
Other (non-default) targets (GUI related I mean), include EFL (Enlightenment Foundation Libraries) and Tk. Both of these have bindings in various languages.
So, in a nutshell, it really doesn't matter what you use, or which programming model (Object-Oriented, Procedural, etc) you prefer. Ubuntu is open to any of them.
For more you can see this site: http://developer.ubuntu.com - which will give you tutorials and other relevant information.