The "strange interlude" is a parody of an eponymous Eugene O'Neill play that was very popular at the time. In it the actors would stop in the middle of a scene and monologue to the audience about how they really felt.
One of my all time favourite Groucho and the magnificent Margaret Dumont scenes. I laughed when I first saw it over 60 years ago and I'm still laughing at it today. Not one comic around nowadays comes even close.
Pre-code Hollywood. This would not have been possible a few years later, once the studios started enforcing the Production Code. (BTW, I say Hollywood, but the film was shot in Astoria, Queens. They would perform the show on Broadway, and shoot the film on days without matinees.)
"That leaves you one up." "He shot her glance....as a smile played around his lips." "If I were Eugene O'Neill I could tell you what I really think of you two. You know your very lucky the theater gild isn't putting this on.....and so is the gild. Pardon me while I have a strange interlude."