There was only one Joe Bloom in the head of household index for New York State in 1920.
1920 New York, the Bronx, ED 46 E. 189th Street Joe Bloom, Head, renting, 31, immigrated 1899, naturalized 1913, Manager (slipper) Rose, wife, 25, immigrated 1904, alien Arthur, Son, 2, born New York Abner Bloom, Father-in-law, 64, immigrated 1899, naturalized 1904, Store (dry goods) Rose, mother-in-law, 62, immigrated 1899, alien, designer (ladies' clothes)
All of the adults are listed as their parents and themselves being born in Austria (Jewish).
There were 4 Harry Bloom's of foreign birth listed in the head-of-household index for the 1920 Illinois Census (Chicago).None of them had a son named Oscar or a wife named Adele. There were no Harakins, and no Blohms that looked to be a match.