John E. Orr
1933-34 St. Rita's - Chicago (High School)
1934-35 St. Rita's - Chicago (High School)
1935-36 St. Rita's - Chicago (High School)
1937-38 St. Benedicts - Kansas (College)
1939-40 Chicago Duffy Florals (Independent)
1942-43 South Bend Studebakers (Independent)
1942-43 Detroit Eagles (Independent)
1942-43 Chicago Studebaker Flyers (NBL)
1943-44 Sheboygan Redskins (NBL)
1944-45 Chicago American Gears (NBL)
1945-46 Chicago American Gears (NBL)
1945-46 Anderson Chiefs (Independent)
1946-47 Chicago Shamrocks (Independent)
1947-48 Chicago Shamrocks (Independent)
1948-49 Chicago Shamrocks (Independent)
1949-50 Chicago Shamrocks (Independent)
1950-51 Fond du Lac (WSBL)
1950-51 Racine Knights (Independent)
A lot of the problem of looking for him is the multitude of article on Johnny Orr, who coached at Michigan.
Orr was a pitcher who played for a few seasons in the Yankees and Cardinals farm systems.
Orr signed with Sheboygan on November 6, 1943.
Another article I found lists an Orr (maybe this one, maybe the other Orr) as playing with the Anderson Packers and an attendee of St. (unreadable) college.
Kokomo Tribune, Nov 21, 1946
Pitched for Akron in 1940.
This is our best bet:
He is in the St Rita's Hall of Fame (which is where we get his middle intial, if it is accurate)
Minor League Baseball Stats
I am now kind of leaning to this guy being John William Orr (1918-1975). I searched for someone born in Chicago who lived in Ohio in 1940 (since Orr was playing baseball in Akron that summer.) Born to Jesse Parker Orr and Mary Ellen Brown. Married Irene Elizabeth Kent in Cleveland in August of 1940. Later married to Patricia (Fitzgerald?), three stepsons; Patrick, Claude, and Terry Fitzgerald.
One possisiblity is John R. Orr (8/13/1918-Feb 1981)