The episode involves a scheme centered around a disco called the Styx. It's well described in a conversation between Diana Prince and Steve Trevor:
Diana: The Styx, its owner is a wealthy socialite named Angelique McKenna. It's become a sort of watering hole for Washington bigwigs.Steve: Providing them access to government officials, from whom Nick Carbone rips off classified data [using his telepathic abilities].Diana: Perfect cover. Who'd suspect a disco fronting for a black market information broker?
This process is shown early in the episode, where Nick steals information about a nuclear bomb from the mind of Anthony Borden, whom a colonel calls "the best nuclear engineer on the east coast." When the prototype malfunctions, Borden can't remember the sequence to disarm it. He explains, "The code, the numbers, everything that mattered, it- it's gone from my mind! I can't remember anything."
Based on this context, I initially thought that the Styx was the river in Greek mythology that causes forgetfulness (which would correspond to the condition of those from whom Nick steals information), but some research revealed that forgetfulness is actually caused by the Lethe. The Styx is the river by which the gods took their oaths. Like the Lethe, though, it's a river that separates the underworld, and I think this holds significance in light of the events of the episode. Similar to how the river Styx marks the underworld's border, the disco Styx represents an intersection between the (presumably law-abiding) government officials and the criminal underworld in which this classified information is stolen and sold. The association between the Styx and the underworld is maintained, but now the underworld is a more metaphorical one.
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I think there's also some significance to Angelique's intense reaction to Nick's shortening her name. In a scene fairly early in the episode, he tells her, "You worry too much, Angie," at which she bristles and replies, "Don't you ever call me that name again." This may seem to be just a matter of strong personal preference, but the contrast with a later scene suggests that Angelique views the shortening of her name in the same way as a limitation of her authority. Near the end of the episode, after Nick has made moves to acquire greater power in their scheme and used his telepathic abilities against one of the Styx's henchmen, he calls her "Angie" twice in the same scene. This time, though, since she's already lost control of her operation to him and she's powerless in his clutches, she offers no resistance.
