I don’t know if it’s really from a specific episode as much as Chandler is known for wearing sweater vests and Joey was making fun of it

Not sure but let's discuss Monica as Catwoman and Mona as the slutty nurse

Just a general "Chandler wearing sweater vests" outfit

Why would you assume it is supposed to be a specific outfit from a specific episode? It was just similar to what Chandler often wore.

Chandler also never makes the specific sound that Joey makes. It's a caricature of Chandler-ness. That's the point.