So if I walk up on any random date can you still get an overnight permit? Or are walk up permits only given to for day hikes the next day?
The overnight permits are less available than day hike, especially in July and August. Check the Unused Permits 2016
page, and from there, the prior few years to see.
Those are the unused permits at the end of the day, and for overnight permits, they start becoming available mid-morning the day before, as groups picking up permits shed their cancellations. At 11 AM on the actual date of entry, the no-shows become available, and there is a drawing of numbers to see who gets first shot at them.