I'd advise a synthetic oil of sorts - Honda recommend a 10w-30 or a 10w-40, depending if it's a V-TEC or V6 engine. Look on the Mobil website for further specific advice or call Honda direct.
Try this website for a more comprehensive look @ Honda oil recommendations:
http://www.bernardiparts.com/Images/Install/OilChart102910.gif
The 2004 Honda Odyssey has single overhead cam (SOHC).
5W30
5w 20
2002 Honda Odyssey uses refigerant type r134a.
it needs 10w-40
The 2011 Honda Odyssey has single overhead cam (SOHC).
The 2014 Honda Odyssey has single overhead cam (SOHC).
The 2009 Honda Odyssey has single overhead cam (SOHC).
The 2006 Honda Odyssey has single overhead cam (SOHC).
The 2001 Honda Odyssey has single overhead cam (SOHC).
The 2003 Honda Odyssey has single overhead cam (SOHC).
The 2012 Honda Odyssey has single overhead cam (SOHC).