Once you have an infestation, or even a few eggs, they will multiply.
So you have to kill every one.
Tranfluthrin is the chemical used in the sachets and wardrobe hangers, it emits a tiny amount of vapour that. in an enclosed space such as a closed box or wardrobe, will kill adults, grubs and eggs over a couple if weeks (I guess the sachets are made so weak that the vapour will not accumulate in the room. It breaks down from sunlight or rain, and dissipates in fresh air).
To get faster results, you can put everything through a tumble drier (it does not need to be wet) and the heat will kill grubs and eggs, then put it all into containers, boxes or plastic bags, sealed with the sachets in (because your house has moths, you can't be sure that eggs will not be laid while you are sorting and folding the clothes), then hoover out and spray your drawers and wardrobes. It takes a few months to be sure you have killed them all. If you leave a few they will multiply again.
They like to live underneath and behind furniture and skirtings, a where they will be undisturbed, and eat wool carpets, so you have to clean all the most difficult places.
Frequent and thorough hoovering is the best way to keep the numbers down, but you need chemicals to kill them all.
You can get non-chemical treatments such as lavender and cedarwood. These do not kill moths but will make your holey clothes smell nice when you throw them in the bin.
An infestation can cause hundreds or thousands of pounds worth of damage, so however nature-friendly you are, you will, in the end, use the chemical, because nothing else works. Once under control you will be OK with hangers in your wardrobes and cupboards, and change them every few months. Put a sachet in the pocket of your best cashmere jacket and tape it into a large, clear plastic bag (you can get them as "recycling bags" on the bin-liner shelf).
The sticky traps are good for showing if you have moths, but they only catch the adults after they have hatched from grubs that have already eaten holes in your clothes. Killing the eggs and grubs is better.
There are various sachets, hangers and strips but check the label to see they contain Transfluthrin