There are two basic categories of household moths, the ones who invade your closet and chew holes in your clothing, and the ones that come from grain foods such as bird seed, as well as many other foods you bring home from the grocery store.
Have you ever walked down an aisle at a grocery store and spotted some moths flying around? I have, as they can be found also in flour, corn meals, and such, and are not always brought home in the bird seed (although it usually is).
Bird seed is harvested and cleaned by the bird food manufacturers using machinery to sift and clean the food before packaging. This does help catch and remove pests/bugs in the seed mix, and some companies do a better job than others. Since the food is going to be eaten by your bird, there are no pesticides used, so quite naturally there are going to be some bugs every once in a while no matter who the company is. Shrink wrapping does help, but does not guarantee you will never see a moth.
When the weather gets really warm, those little moth larvae seem to hatch out at an alarming rate and appear everywhere. Freezing your bird seed for at least 48 hours as soon as you purchase it will help kill some of the pests in the seed mix. Don't forget to do this also with wild bird seed if feed the outside birds as wild bird seed mixes are usually not cleaned thoroughly at all.
Keeping the seed in the freezer and only taking out what you need each week helps. Keep the food in a sealed bag or plastic container during the week as you use it. If you do have a moth outbreak, don't panic, simply control it to eliminate it with a few easy steps.
First step, go on the hunt to vacuum as many moths as you can find. Then thoroughly check your ceilings. Yes those sneaky moths lay their larvae on the ceiling and you will find tiny while larvae or small worms (yes I know yuck) hanging out ready to hatch and start the cycle all over again. Vacuum them off the ceiling wherever you find them. Vacuuming may be a daily chore for a while until you can get things under control.
The moth pest traps you can purchase from stores such as the moth trops available at the Nature Chest, do in fact attract and catch the adult flying moths. They use a pheromone that attracts the moths into a sticky trap. These moth traps are completely safe to use around your birds but you will want to make sure your bird cannot reach the sticky trap because they are really really sticky.
However, do not make the mistake of thinking one little trap is going to handle a multitude of moths. If you have a lot of moths to eradicate, you may need to place traps in several locations and check daily. If the trap is not catching anything, then move it to a different location. Depending on how many moths are flying around your home, the traps can fill within a month, or may last up to 6 months.
I have heard of the use of homemade moth-repelling sachets made up of some of the following: bay leaves, cinnamon sticks, cloves, eucalyptus leaves, lavender, pepper corns, or dried lemon peel. I believe these remedies would work better for closet moths, more than preventing or chasing away kitchen/aviary type moths. However, they would make your home smell really good.
Just remember moths and other bugs found in seed mixes are in fact high in protein, so if your bird eats one, it's okay, and no they don't bite, and yes they are annoying. Just say "yuck" and tell your bird not to eat any more.