It's not easy to study while severely depressed and anxious. I find that it helps to list what needs to be done and to prioritize those tasks, like you've been doing. I also make sure to allow a realistic amount of time to complete the tasks. I recently had 5 tests in two weeks. I was out of my mind with anxiety and stress! I identified exactly what I could skim over and what needed a closer look. Then I wrote up a schedule for the tasks so that I would complete them by test day. Just identifying what needed to be done and setting a schedule for them eased my anxiety. Then getting to work on completing the tasks eased my anxiety and stress further. Having a plan and working on it really help me.
I did an okay job of sticking to the schedule. I ended up cramming but I did cover what I needed to cover and did alright on my tests. Some things took longer than originally anticipated, so I adjusted my schedule. I didn't let myself beat myself up for not sticking to the schedule.

The schedule was just a guideline.
What also helped a whole lot was to go to a coffee shop to study. They know me well at Panera Bread! Then I didn't have any distractions. Since I was in public, I couldn't take a nap. I did have to leave my cell phone in the car. The game apps are rather distracting...
When anxiety has a really strong hold on me, I find that doing something that completely commands all of my attention for awhile helps break the hold. Going to a movie, swimming in the ocean, working out really hard, playing music so loud that I can't think, screaming while driving. Something that distracts me utterly and completely.
If all else fails, I take half a Xanax. I'm such a lightweight. I also take Prozac, which I've come to realize really ratchets up the anxiety and xanax doesn't do anything for it. So, I cut back on Prozac in order to lower my anxiety enough to study. (My doctor is taking me off it now since the side effects are greater than the benefits.)
I also like to drink Celestial Seasonings' Tension Tamer tea. It takes the edge off anxiety for me. It's like a brain tonic. It's something to drink, but it won't have the adverse effects of drinking gallons of coffee. I tend to eat and drink when I get stressed. Drinking herbal tea is a way to self-soothe.
I hope that helps. I feel your pain. Been there and will be there again in a few more weeks. Remember - breathe!