Learn English – What does “they were taken for being taken in” mean

As you might have guessed, the quote from the film suggests, that the stench from the flatulence is so bad, it even kills an animal.

As far as I know, this is not a synonym for passing gas, it is just a movie quote. Therefore, I would say that anyone remembering the scene in the movie would understand the idiom. Also, if the idiom is presented in the right context, people might also be able to understand what you are talking about.

For example

• [awful stench can be smelled]

• You: "Puh, I just had to kill that dog."

Tough the two sayings refer to similar actions, their meanings depends on their origin and their usage.

As for have an ax to grind, it appears that the notion of "having ulterior motives" comes from:

• The story is a cautionary fable concerning the author's recounting of an incident from his youth, where a passing stranger takes advantage of him and, by flattering him, dupes him into turning a grindstone to sharpen the stranger's axe. Miner then uses having an axe to grind as a metaphor for having an ulterior motive:

  • When I see a man holding a fat office, sounding 'the horn on the borders' to call the people to support the man on whom he depends for his office. Well, thinks I, no wonder the man is zealous in the cause, he evidently has an axe to grind."

(The Phrase Finder)

Sharpening a saw, refers to a story of a frustrated lumberjack and conveys the notion that:

• We get frustrated by life and our inability to cope, but instead of developing ourselves and taking the time to become more effective, we keep struggling with a blunt saw.

(betterlifecoachingblog.com)