It appears that Oliver was a few generations removed from Germany:
1930 Warren Co. census lists an Oliver age 7, son of William & Hulda Backhaus, both 36, all born Mo.
1920 Warren Co. census lists William 26 and Hulda 25, both born Mo.
1910 St Charles Co. census lists William 17 Mo., son of Henry Backhaus 48 Mo and Lizzie 43 Mo, parents of both born Germany.
1900 St Charles Co. census lists William b. Apr 1893 Mo., son of Henry Backhaus b. Jan 1863 Mo and Lizzie b. Jun 1867
1880 St Charles Co. census lists Henry 18 Mo son of Henry 56 and Elisebeth 50 both born Hanover
1870 St Charles Co. census lists Henry 8 Mo son of Henry 49 and Elisabeth 37 both born Hanover
1860 St Charles Co. census lists Heinrich 35 and Elisabeth 24 both born Hannover, their oldest child August age 4
St Louis marriages lists Bernhard Heinrich Backhaus to Maria Elisabeth Done 15 Apr 1855.
"Hannover" in the censuses almost always meant the old Kingdom/Province of Hannover, and not the city therein, and to trace the family further in Germany, the Hannover village or parish will be needed.