Properly maintained (according to MFG specs or better) any Honda engine should last well over 200,000 miles before it shows any signs of significant wear of internal engine parts. Of course, normal wear/tear issues might arise before then.
The 2004 Honda Odyssey has a V6 engine.
The 2003 Honda Odyssey has a V6 engine.
The 2005 Honda Odyssey has a V6 engine.
The 2008 Honda Odyssey has a V6 engine.
The 2009 Honda Odyssey has a V6 engine.
The 2011 Honda Odyssey has a V6 engine.
The 2010 Honda Odyssey has a V6 engine.
The 2012 Honda Odyssey has a V6 engine.
The 2007 Honda Odyssey has a V6 engine.
The 2013 Honda Odyssey has a V6 engine.
The 2014 Honda Odyssey has a V6 engine.
The 2001 Honda Odyssey has a V6 engine.