When someone says the words quote or unquote or quote/unquote, they should be surrounded by punctuation, AND the word or words that follow should still be quoted. There is no rule in the literature that supports leaving out the quote marks because the words are said. It is not an either/or.
The words quote/unquote have a slash mark between them.
...is a, quote, "monster" when he drinks.
...sent a, quote/unquote, "zinger" to her.
Happy punctuating!
Margie