What was the "Whore of Asia" (Shanghai) like during the 1920s/30s, especially regarding the activities that gave it that nickname? How did life change, if at all, during that time period?

The phrase you are looking for is "Whore of the Orient".

I am no historian but I figured I might be able to help with your google searches if I corrected that. It's hard to find any real documentation on the phrase itself as the creators of that game "L.A. Noire" are making a game for 2015 called "Whore of the Orient". If you change your search results to only show web results from before 2010 you may be able to find more solid information. Like this

Hope this helps in your search for answers!

Edit: Well I couldn't stop reading about it... This is the best answer I could find. It wasn't called that in the 1910's yet, it wasnt until the end of the Qing dynesty in 1911 source. While MANY websites take the easy route of saying its because of widespread prostitution. It looks like several sources including this one claim that because trade was so one sided with the British doing all the buying with nothing to sell. The British merchants would go to India trade silver for opium at a huge profit and then the merchants would take that opium and use it as a trade good or currency to purchase things in Shanghai. Just as an individual may exchange services with certain prostitutes for drugs. Like a proverbial "whore", Shanghai would give you what you wanted (tea, silk, and porcelain) you just needed what she wanted in exchange... and in the 1920-1930's Shanghai wanted Opium and it wanted everything british ships could carry.

I hope that I could shed some light on your question. I am new to world history but reading this sub is helping :)