Daily, the cages get a quick dusting and the top layer of paper gets pulled at bedtime. That way I not only start/end each day with a clean cage, I know where the bird actually slept.
Weekly, I use PoopOff (non-fraganced enzymatic cleaner) to clean poopy perches, bars, grates and toys. Now is a good time to exchange toys and forage baskets. Each tray gets 14 layers of paper, so two can be removed daily.
Quarterly, I use F10 (disinfectant) to disinfect the clean cage.
Annually, the cages are taken outside for a thorough cleaning with vinegar and water, sun drying, then spraying with F10 and, again, sun drying.
I've found the key is a regular and scheduled cleaning! I've heard of the bathtub thing but prefer to clean the cages in place weekly with a summer scrub. I use a variety of tools including leftover toothbrushes, washcloths and shower scrubbers (like loofahs).