I have used deep litter both on a commercial scale under thousands of chooks and now, under 50.
Hay is no good at all because it is not absorbent and it is rather nutritious (which is the whole point of it) and grows moulds and bad things too easily. The ammonia is produced by the anaerobic breakdown of wet bedding and raw dung.
Straw is little better in a deep litter system unless you add to it daily which is not the point of 'deep litter' as we understand it nowadays but it does have its uses - as in the Balfour system: Google it!
For a deep litter system use wood shavings. Put down at least 6 inches of it. The chooks will move it about sufficiently to aerate it and it will have time to dry.
Now in a small chook house this may not work because they are pooing all night - but you have a dropping board to catch that, and they may not rootle about so much in their sleeping quarters.
The system relies on the chooks moving the litter and on it remaining dry. So always remove heavily soiled or very wet litter (say under a leaking drinker) which is obviously not drying.
We have some small problems during our winters when the litter may not fully be dry and we have to manually turn it now and again to encourage the chickens to scratch around some more. We clear it out when the depth becomes a nuisance - ie when you can no longer close the door or there's no room under the ceiling!!!!!!

This comes to about once per year.