Post-doc applications I am having terrible experiences with my PhD program. I have no feedback and no supervision on anything. I have been working with other people in other departments so that I can get proper training before I graduate. Recently, I realize that if I apply for a post-doc fellowship and stay here, I can actually learn more about these techniques. But I heard from many people that staying in the same university or with the same people that you worked with is not possible. Does anyone have any opinions on this? I have been travelling around throughout my entire university journey. This will be first time that I will be staying in a place for two different positions. Is it still a no?
One of the biggest reasons for moving around is so that you learn, over time, a variety of techniques and viewpoints. If you stay in a place too long as a student, you may already know whatever it is that they are able to teach you. 

But that isn't your situation. You are moving to a new situation within the university, broadening your horizons with these other people. My guess is that it would be good to take advantage of the situation. You also, as you say, seen a variety of different faculties already, so it is less important to move on than if your education had all been in one place. 

Don't stay forever, of course, but learn what you can from the people able to give it.