Roaches are mutated cockroaches that appear in the shelter if they are ignored in the trash can event. They can make certain family members sick, and can be killed with either the Boy Scout Handbook, the Rifle, or the Bug Spray.
When you play in the Dolores DLC and have the harmonica and play it the roaches will start dancing and will eventually bring out a soup can. Use a book to kill them
If you get the disco roaches scenario, always use the harmonica. There will be a following event asking if you can play it. Say yes, and they will bring a soup can and a water. No family members will ever get sick from any roach scenario, except where Timmy and Dolores fight over the atomic ants in Timmy's pocket.