The life expectancy of a well designed Japanese engine will commonly be between 150,000 and 200,000 miles. But the automatic transmissions begin to fail at around 140,000 miles; and that can be a major cost to repair. If this concerns you; you can avoid this problem by only buying a vehicle with a manual transmission. They are listed in the parts catalogs for these models. However, I doubt that you'll find a Sienna or Odyssey with a manual transmission. What does this say about the values of the people who buy those vehicles? You may be more likely to find a Pilot with a manual transmission; but it still would be very difficult to find. So this is what you're up against. Unless you must have 4 wheel or all wheel drive; I would also avoid vehicles with those features; because it complicates repairs, reduces fuel economy and adds many parts to the vehicle which can potentially fail.
Since most people drive about 12,000 miles per year; if you hope to have 4 or more trouble free years of service, and decide to get a vehicle with an automatic; I would try to avoid any with more than 110,000 miles on them.
If this becomes too impractical to fit into your budget; you still might be able to achieve a similar goal by buying a smaller vehicle. Toyota manufactures the RAV4; which is a smaller vehicle of this type, and costs considerably less. I have high regard for this model; which has grown larger in recent years (along with its price tag).
Toyota also manufactures a still smaller line of vehicles called Scion. There are two wagons in that line; the xB and xD. The xD is a more recent model (2008 and newer); and may still be too expensive for your budget; but the xB is larger than the xD, has been sold since 2004, and is priced considerably lower in used versions; see the following Edmunds link: (http://www.edmunds.com/scion/xb/2005/?s
u...). These vehicles cost about $15,000 to $17,000 NEW.
Whatever you do; please follow our long standing advice, and do not buy ANY vehicle; regardless of how it is represented or warrantied, without first having it thoroughly inspected and evaluated by an experienced, honest, professional mechanic or a diagnostic center like the ones the AAA operates nationwide. The cost of this service will be more than offset by avoiding pitfalls and potential regrets. There are all too many used vehicles out there which were reconstructed after being wrecked; or were bought at an auction after having been stolen, stripped, or abused; or were repaired by unskilled or unscrupulous people. You wouldn't want to own one of those; believe me.