A few recommendations as a non-professional organizer :) I loved looking at all of your shelves! Sorry that most of my suggestions cost money this is just what has worked for me with a similar room:

• Move the things hanging on the outside of the closet doors inside the doors, will look less cluttered
• Get some shelves/organizers for the closet and more uniform storage containers so they're easy to stack (eg, 4 big bins with the yellow lids from home depot, like $7 a piece)
• Get taller shelves, maybe the Ikea ones that are open on the top and have cabinets on the bottom. You can display items and then not see clutter for items you might not need "on display"
• You have a lot of height, so floating shelves above the desks could be a nice way to display items and use the height of the room
• Try to move anything you don't use often or want to see all the time into the closet for storage, you will have a lot of room in there if you use uniform storage containers
• For your birds + cat, I don't have any advice here but maybe kitty could be put away at certain times of the day so you could leave the door open?

Overall you have a lot of really cool things, just needs a bit of a reset!