Enormous—very big. Compared to a flea, an elephant is enormous.
Enormity—very bad, especially in violation of morals. The enormity of child abuse is comparable to the enormity of spousal abuse.
Don’t use “enormity” when you are talking about size! “Enormity” is a noun, “enormous” is an adjective. If you need a fancy noun for “enormous,” use “immensity.” (If you need a fancy adjective for “enormity,” use “egregious.”)