Neither newspaper or towels absorb any odor. The towel will absorb urine but that allows that very strong ammonia odor of the urine to be continually inhaled by the rabbits. So this isn't ideal or healthy.
Wood pellets (not shavings) work wonders for absorbing both urine and the odor of urine. Those wood pellets can be placed in the tray in place of newspaper or towels. (newspaper under the wood pellets might make it easier to clean -- not sure though)
If you are using a litter box, I'd suggest you also put a layer of wood pellets under the hay in the box. This will absorb that odor and make the box last longer between cleanings. Once your rabbit gets the hang of the litter box, you won't need anything under the wire. In fact, you won't need a wire bottom at all. The whole floor can then be solid. (With hay in the litter box, you'll want to add fresh hay on top every day so there is always fresh hay for munching.)
So, once litter trained, your work will be much, much easier. The only thing you'll need to clean out is the litter box with maybe a weekly sweep out of the rest of the cage. The litter box itself should be able to last about a week between cleanings with one rabbit, about 3 days with 2 rabbits --
provided the litter box is large and the hay is refreshed every day.
Wood pellets (not shavings) can be found at hardware stores and sold for use in wood pellet stoves OR they can be found at feed stores and sold for use in horse stalls as bedding. Be sure it is the compressed wood pellets (not crumbled).
My rabbits are indoors, but I will attach a photo of their litter box set up as an example. Please note
(1) the size of the box itself (important for ease of maintenance). Smaller boxes won't last as long between cleaning and will require more work. Also note
(2) that since my rabbits are indoors, when I say that it can last a week (w/ 1 rabbit) before smelling, that means there really is
no odor in the indoor space until a week has passed.
Wood pellets is a good idea for the litter box though!
