You picked the right van, but the wrong year. Best years for the Honda Odyssey were 02-04. But to avoid an abused vehicle, or a vehicle that has been in a accident, spend the 80.00 bucks and take it to a quality mechanic to check for problems. Also, one owner cars with records are a big plus.
Your best bet in any used car is always a low-mileage, former rental vehicle. These cars are serviced regularly, and any defects are immediately taken care of.
Having worked for a dealership, I can assure you that lease returns and demos are some of the very worst cars you can get. Many people lease a car for two or three years, and never even bother to change the oil, because they know it's going to be returned at the end of the lease. Salesman's demos are the worst of all. They are abused beyond imagining.
And those "one-owner with all the records" cars... well... BEWARE. I've seen those with falsified records and inaccurate mileage. Private owners are under no obligation to tell the truth, and it's virtually impossible to take any action if you do get taken. Only buy from a private party IF you know the person. Otherwise, you have literally no idea what you are getting. One teen-aged driver in a family can do a car more harm than 1000 rental drivers.
My family has bought three former rentals. All were fully loaded (most rental cars, contrary to myth are NOT "strippers") and one was a sports car. All were absolutely flawless, and never had a single problem.
Finally, I'd advise anyone looking for long-term reliability to avoid any Japanese brand. Modern domestics are far more durable in the long run, and usually cheaper to repair as well. Having had both, I'd take a good used domestic any day. Studies have shown that the best all-around buy in a used vehicle is a 4-year-old Ford or Chevy.