[Answered ]-Can a older version of django project work on higher version?

You’re right, the django migration is something not very documented.
In my opinion, the best thing you can do to be quick and secure, is:

1. Check all the major changes between Django 1.4 and 1.7 (look for changelog and Djang website).
2. Take a look to your code to be aware of what part will be obsolete after the migration.
3. Do the migration, in a non-critic environment of course. For this purpose, don’t touch to your code first, just upgrade the Django version
4. Fix your code until it works perfectly (run unit tests if you have some).
5. You’re ready to do the migration in a production environment.

I did it between Django 1.6 and Django 1.7 (and migrating from Python 2.x to 3.x in the same time). It was easier than I had imagined. However, Django 1.4 to 1.7 could be a little bit longer, but nothing hard.