OASIS Hong Kong Airlines, Hongkong, 2005-2008.   -   #1:

OASIS Airlines, Madrid, Spain. Founded 1986 as Andalusair, renamed 1987 after majority stake taken by Oasis hotel group. Ceased operations 1995.    #1,          #6              and          #2:

OCEAN AIR, Sao Paulo, Brazil, 1998-2010 rebranded as Avianca Brazil (q.v.).   #3, #5, #1 and #2:

Odyssey International, Toronto, Canada, 1988 - 1990.    - with thanks to Lu Lloyd -#1:

Okay Airways, Beijing/Tianjin, China, founded 2004.
- with thanks to Dr. David Bradford-  #1, -and to Andrew Yang - #4   and   #5

Olympic Airways, Athens, Greece, 1957-2003,   -  #13 and   #1/#2/#3/#6(variations); 
Olympic Airlines,  2003-2009.                                                                       #16:

Olympic Air, Athens, Greece, as of 2009.      #20   and       #20A:

OMAN AIR, Muscat, founded 1993. 
-  #6,    #8/#9(flat base, diff maker)  and  #10(pointed base),  #11(diff maker at base):

-   #3,                                                            #5a,                                        #2:

  -   #7:

OMNI Air International, Tulsa, Oklahoma, USA, founded 1983.     - #1,             #3:

OMNI Aviacao e Tecnologia, Oeiras, Portugal, founded 1988.  -  #1:

Onur Air, Istanbul, Turkey, founded 1992.
  -  #3,                        #5/ #6(diff. maker),                                      and  #2:

Orbest Orizonia Airlines, Palma de M., Spain, founded 2011 by renaming from Iberworld (q.v.),
ceased operations 2013. Remainig aircrafts were transfered to sister Company Orbest Portugal(q.v.).
- #2:

Orbest Portugal, Lisbon, founded 2007.    - #1:

ORC - Oriental Air Bridge, Omura-Nagasaki, Japan. Founded 2001 by renaming from Nagasaki Airways.   
    -                              #1,                               #2:

ORION Airways, Manchester, UK, 1978 - 1989 merged into Britannia (q.v.).    -  # 1 and  #2: