The drunkest or most fucked up person in your group at any given moment.
Look at Jesse, he is a real Greasy Tony right now. How many Budweisers did he drink?
A greasy Tony is when a guy sticks his dick in old fry oil and plays bongos with his penis on his partner's cheeks
Jim: hey I just gave Samantha a greasy Tony in the Wendy's bathroom
Dave: is that the Korean ladyboy
Jim: yup it took two napkins to get the grease off