Something grungy is very dirty, like the old sweatshirt that your dog dragged outside and used as a bed.
Are your hands absolutely filthy after tinkering with the engine of your old car? Then they're grungy, so ingrained with dirt and oil that you'll have to scrub to get them clean. Dirty and sloppy things are grungy too, like the grungy outfit you wear when you spend the day taking care of your uncle's pet pigs. This informal American slang word is probably influenced by both dingy and grubby.