Find a semi and 'draft'... Sounds dangerous but its about the only way.
We have a 2006 Odyssey and love the van, but hate those pit stops on road trips. It doesn't bother me around town; but we sold a Grand Cherokee for this van because it was rated in the high 20's (I forget now). I've changed my driving style and our cargo and it yields some results.
The Odyssey, and every other smaller engine, has a greater percentage loss with heavier loads. So if you've packed 8 adults in the van don't expect good fuel economy. We recently made a trip from the mountains (so our elevation loss pretty much made the whole trip down hill) with 4 adults and 2 children and we got 22 mpg. I was pleasantly surprised but I don't know if driving 60-65mph was worth the kids asking "are we there yet". =)
In summary, you can expect just over 20 if you're driving slow and are mindful of the contents of your van.
The EPA mileage estimate for the 2013 Honda Odyssey is 18 mpg in the city, 27 mpg on the highway.
The EPA mileage estimate for the 2009 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2010 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2006 Honda Odyssey is 17 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2008 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2011 Honda Odyssey is 18 mpg in the city, 27 mpg on the highway.
The EPA mileage estimate for the 2014 Honda Odyssey is 19 mpg in the city, 28 mpg on the highway.
The EPA mileage estimate for the 2005 Honda Odyssey is 17 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2004 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2002 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2001 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.
The EPA mileage estimate for the 2003 Honda Odyssey is 16 mpg in the city, 23 mpg on the highway.