In the (highly improbable) situation where you have designers with each of those job titles, and none of them are directly collaborating or working in tandem, and setting aside the many other job titles that could overlap partially or completely with those listed here -- information architect, product architect, product management, information design...
...With those caveats, I'd put them in this order:
- Product designer "What does the product do?"
- User experience designer "How should it do that?" in terms of overall product architecture and workflow.
- Interaction designer "How should it do that?" at the per-page or per-feature level of detail.
- User interface designer "How should it do that?" at the per-widget level of detail.
- Graphic designer "What should it all look like?"
That said, if you really did silo these tasks separately like this, you'd be very likely to wind up with a terribly disjointed product -- design is an inherently holistic task; all the parts need to coordinate and work together. (I don't subscribe to the There Can Be Only One Designer school of thought, but you do need a clear, singular vision of how all the parts should fit together in order for people to not wind up pulling in different directions.)
Also: with the possible exception of the last one, these job titles do not in any way have universally-agreed-upon definitions. ("Interaction designer" and "User interface designer" in particular are effectively interchangeable titles -- the distinction I made between them here is largely an artifact of how the question was structured.)
And there's a ton of overlap between these roles in any real-world situation: any individual designer will wind up doing some part of all of these tasks, and the scope of their design responsibilities will usually have more to do with seniority and talent than with their specific job title.