Whenever we flush the toilet, the pipes make a loud gurgling sound. They do not appear clogged but we snaked via the bathtub drain just in case. It was clear. So our theory is that... (I know this sounds crazy)... Squirrels have dropped nuts into the roof vent leading to the toilet. Is there away of removing the debries without removing the toilet and part of the wall? There are so many 90's that we can't get the wire snake down the vent from the roof. The vent also branches off to the tub so water pressure snake and vacume will not work.

"Squirrels have dropped nuts into the roof vent leading to the toilet."
And you haven't put screens over the vents yet to prevent this from happening?
I don't care how many 90's and revents there are in a vent line I have yet to find one that I couldn't get a snake down to clear. Get a professional in to check the attic to see if he can cut in a place to snake from. This problem ill continue until you do. Regards, Tom