Regarding the discrepancy between Reva Osernoff living with the Axel family in 1920 and 1930 and later Reva O. Axel in her marriage record, have you considered the possibility that Reva Osernoff married one of the Axel brothers and then was widowed? That would account for both the name change and the middle initial O. Have you located death records and/or obituaries for all of the male Axels in these census records? Perhaps one lists a surviving spouse with a name similar to Reva.
Researching the variations and possible alternative transliterations of her name (Reva/Reve/Riva Osernoff/Osenroff/Osinov etc.), we find a declaration of intention for naturalization for Reva Osernoff dated 24 Sept 1926. This declaration says she was born in Starai Russa, Russia on 8 June 1904 and resides (as of 1926) at 2435 Dickens Ave, Far Rockaway, NY. She emigrated from Hamburg, Germany on the Imperator in October 1913, arriving at the port of New York on or about the 30th October 1913.
Searching the immigration records, we find a likely candidate. On the New York side, the Imperator arrived at the Port of New York on 29 October 1913, having sailed from Hamburg on 22 Okt 1913. Among the passengers is a 9-year-old Hebrew Russian girl (born ~1904) named Riva or Rive, born in St. Petersburg, Russia. Her last name was originally written Asernova, but that is scratched out and Oscinofsky is penciled above. If you pronounce either of those, they are close to Osernoff. According to this two-page record, Riva last lived in Samolta, Russia.
In at least three places in this immigration record, Riva's line 15 is tied to line 14 with a curly brace, seeming to indicate that lines 14 and 15 are traveling together. Line 14 is Edna Margolies, age 25, a Hebrew Russian woman born in St. Petersburg, Russia, and living in Brooklyn, NY, with her husband H Margolies. The nearest relative of both Edna and Riva, connected by a curly brace, is "parents: S. Plattstein (?)," St. Petersburg. It appears that there was another name on the page that was cut off by the imaging. As evidence for enough space for a missing name, there is a stamp that presumably says "NON IMMIGRANT ALIEN" but all you can read is "NON IM" on one page and "NT ALIEN" on the other.
On the Hamburg side, we find the emigration record from Hamburg. On line 459 is Edna Margolies, 25, an American (?) living in Brooklyn, and on line 479 is Rieva/Riva/Rieve/Rive Asernova, 9, a Russian from Star?yruska (?). There's no explanation why the two are not shown traveling together on the outbound side.
Starai Russa or Staraya Russa is a town in Novgorod Oblast, about 300 km south of St. Petersburg.
I haven't been able to find a record of Edna's marriage to Mr. Margolies (or Margolis or Margulies etc.). I have found a Harry Margolies, b. 1888, living in Brooklyn, and a Bernard Margolis in Brooklyn with wife Edna; either or neither of these could be relevant.
If this were my family, I would trace the Axel family forward to find out what happened to them, and I would attempt to figure out how Margolies fits in. Also, where does Plattstein come from, and is there another parent name cut off from the original record?
"New York, County Naturalization Records, 1791-1980," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:QR37-6Y6Z : 11 December 2020), Reva Osernoff, 1926; citing Naturalization, Queens, New York City, New York, United States, citing multiple County Clerk offices of New York; FHL microfilm 005412045.
Ancestry.com. New York, U.S., Arriving Passenger and Crew Lists (including Castle Garden and Ellis Island), 1820-1957 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.
Staatsarchiv Hamburg. Hamburg Passenger Lists, 1850-1934 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2008.
Original data:Staatsarchiv Hamburg, Bestand: 373-7 I, VIII (Auswanderungsamt I). Mikrofilmrollen K 1701 - K 2008, S 17363 - S 17383, 13116 - 13183.