WOW! This used to be my life. I decided to take the simpler way out though and pace myself. Regardless though, I understand what you mean about the stress and not being able to actually do anything. Once you become worn out or too overwhelmed, you're constantly tired and your brain doesn't allow you to focus because it thinks you need rest, regardless of how much sleep you're actually getting. I figure out a way to make things work, and I'm not sure if it'll work for you but it's worth a try.
Primarily, try to tell yourself that you have time and that you can accomplish this, you just need to take it slowly. Then you need to make a calendar, or get one - and write out the due dates. Figure out how much time you have until you need to hand these things in or prepare for them (if they're tests). Once you've got an outline of how much time you've got until they are due, look at them carefully. I used to write out the requirements in my own words with ideas and notes on a separate piece of paper and attach it to the assignment so when you go back to it, you remember your initial reactions when reading the outline/expectations.
Take on your work one step at a time. Brainstorm for all of them. But I don't suggest that you work on one until you're done and then move on. I suggest that you work on all of them, slowly - especially if they are all due around the same time. For example, if you know that you have 6 hours to do work towards any of these assignments, dedicate 3 to one assignment and 3 to another - or divided however it works for you best. That way, you can work on it and leave it - and go back to it another day. That ensures that your ideas don't block themselves - I don't know if it's happened to you, but it used to happen to me a lot - I would write an entire essay and when I went back a few days later, I wouldn't understand my own points. Because when you're writing, everything makes sense, because you're the one that knows what you're writing but you need to make sure that when you're done you leave it for a couple of days to ensure that your points make sense.
Again, I don't know if this will work for you but it's how I used to get through all my university readings/assignments for years. Good luck