The following passage is from a BBC news article.
Prescription pill abuse is taking off in Sudan's conservative society, partly because it lacks the social stigma and pungent, giveaway odour of alcohol and cannabis.
I get the overall meaning of it. However, I do not understand the grammar structure of giveaway odour of alcohol and cannabis. Shouldn't there be and before giveaway odour of alcohol, or is the last comma being used as gapping comma?
This is not really a gapping comma, although it looks quite like one.
As what @Patrick Stevens has mentioned, it's a comma separating two coordinate adjectives.
A gapping comma indicates that you have decided not to repeat some words which have already occurred in the sentence
Although "pungent" and "giveaway odour" have similar meanings, both refer to the "alcohol" and "cannabis", but both are adjectives. It is said that
A comma should be placed between two adjectives (of equal rank) that describe the same noun
In this context, this fulfills the above condition. Although I am not sure of the name of putting a comma between two coordinate adjectives.
And no, I do no think you can write
'.... because it lacks the social stigma and pungent, AND giveaway odour of alcohol and cannabis.'
First, you are using 3 "and" in a sentence and 2 "and" to describe the same two nouns, which is quite repetitive. So you're better off using that comma in between.
It's not really a gapping comma. It's a comma separating two coordinate adjectives, which is a standard construction. I can't actually find an authoritative reference for the rules here, but see e.g. a question on the difference between coordinate and cumulative adjectives.
A couple of alternatives you mentioned:
"… because it lacks the social stigma and pungent, and giveaway odour of alcohol and cannabis"
This one is at best confusing and at worst wrong. I bet a reader would attempt to parse this nonsensically: "because it lacks the social stigma and pungent. Additionally, giveaway…", mistaking the comma for a clause separator. At best, this is a garden-path sentence.
"… because it lacks the social stigma and pungent and giveaway odour of alcohol and cannabis"
This is less wrong, but I find it aesthetically displeasing. The two instances of the word "and" serve different purposes: one separates the elements of a list of modifying adjectives ("pungent", "giveaway"), and one separates the elements of a list of modified noun phrases ("stigma", "odour of alcohol"). One of the reasons we have punctuation is to give us other options when using mere words would cause us to repeat ourselves.
