Use grotesque to describe things that are very strange and ugly in an unnatural way. If something "grosses you out," you can safely refer to it as grotesque.
Grotesque also refers to a style of art that uses odd and fanciful combinations of natural, human, and animal forms. The original reference was to cave paintings found in ancient Roman ruins. Our English word is from French, from Italian grottesca pittura "a cave painting," from grotta "cave." Italian grotta is the source of our English word grotto.