First on the clothes moth. It's always hard to know why any pest has these surges and declines in their abundance. Outdoors we can take the easy road and blame the weather, but this often is a causal factor when we have excessive rains or drought, a really cold, long winter or a mild one and an early spring. Overwintering bugs are going to react to these changes from "normal", as are the things they feed on. Indoors it may be harder to find the reason, just as we saw with the difficulty of pinning down the exact reason(s) for the upsurge in Bed Bugs in the last 10 years. Maybe one reason is the same for both, and that could be the reduced use of insecticides indoors, enabling these bugs that might have been killed in the past to survive and reproduce more readily. Perhaps there is some increase in the use of wool fibers for clothing or blankets, or some other materials that these moths would eat, giving them more opportunities to do well indoors. Looking for that cause would be interesting for you. 

The Brown House Moth - Hoffmanophila pseudospretella - has actually been present in North America for probably a hundred years or longer and it is a much more common moth in Europe. In addition to various bits of organic debris that may be eaten it also will feed on stored food products such as dry pet foods, cereals, baking mixes, and grains such as rice or corn. I also may feed on animal products like the typical clothes moths do, so fur, feathers, and woolen materials as well as leftover stuff in animal nests and bird nests. Clearly this is a pretty diverse moth, and this leads to some difficulty in controlling it because finding and dealing with the SOURCE is necessary. I think fumigation would be an extreme measure to go to, but if the most thorough search and inspection you can do does not turn up that source then fumigating the whole structure certainly would kill them.

The problem with fumigation is that it does nothing to eliminate the contributing condition, which is some acceptable food material that these moths have discovered indoors and whose larvae are now busy eating (a.k.a. "recycling") that material. If that material is still there other moths or carpet beetles will eventually find it too and the problem can start up once more. Try to narrow down where the moths are being found most commonly in the structure and then start with the easy things first - clothes and blankets, stored food products, and then progress to the attic for a look for animal nests. It could be that something died in a wall void or an inaccessible place in the attic and you are not going to be able to remove it, but more often it will be something in a place where it can be found and disposed of.