Suppose If I convert any project from SP2007 to SP2010 or SP2003 to SP2007 or SP2010, all my code written in that should convert as per the latest version? Or do I need any further effort to put on this? I dont have such scenarios to test, thats why I am asking here to know about it.
You will almost certainly need to make modifications. Migration tools will only work perfectly on the most simple applications, and even they can have problems. The more features of the core libraries that your systems make use of, and the more assumptions that you have been working with about "the way things work" in SP, the more problems you will have.