Pantry moths...

[nzoomed]

I believe that they can pierce their way through plastic bags. Containers should be safe if they are truly air tight - most aren't though and those tiny gaps will let them through.

Best way to deal with them is simply put the contaminated foodstuffs into the freezer, then do the clean out as above. Leave the food in the freezer a week then  decide what you want to keep. The moths are harmless. It's only our cultural distaste of them that makes us shudder at the thought of them.

Future prevention can be achieved if you freeze goods on arrival from the supermarket. Even keep grain-based goods in the freezer permanently if your problem is ongoing.

Yeah they are harmless, but they ruin your food.
It's said that most of us have eaten the caterpillars at some time in our lives, I first discovered them in my bowl of cereal after all.
The freezer method sounds like a good idea, but it should also pay to check afterwards how much of th food is spoilt. When I opened up the bag of oats it was almost dust! They must have been in there for some time in the store before I bought it home.
I have a friend that seals anything like this in mylar foil bags and that way it keeps everything out until she is ready to use it.
All the stuff in plastic is OK with the exception of items that had already been opened. Everything in paper bags was chewed through.
I think they could make their way through some types of plastic if it was thin enough. I also noticed that many brands of pasta and rice have holes already punched in the bags, which im not sure what the exact reason is for but probably to allow it to breathe or something.