If you read a lot of cooking magazines, you might find a food described as having an “unctuous mouth feel” or “unctuous texture.” It means that the food coats the tongue with a smooth, almost oily layer of flavor. When the word applies to food, it’s a good thing. It’s not a good thing when applied to a person. Someone with a smooth, oily manner is usually not to be trusted. To speak in an unctuous fashion means to be overly but insincerely polite and flattering or ingratiating. You might call a person who speaks like that “smarmy.”
Example: “The shop clerk tried to make more sales with his unctuous treatment of the customers, but all except the most fatuous saw right through him.”