ndb - you should stick with 35psi cold inflation (measure in the morning before the car is driven). Typically, 35psi tire will become about 38-40psi after being driven for a while.
Mach1351must - replacing the tires with lower profile will help a little bit because less side wall equals to less flexing, but Odyssey is such a big car that it would requires better shocks/springs to improve its handling. As for tire wear, it is the exact opposite of handling. Better handling tires means softer compound which don't last long, on the other hand, long lasting tires such as Symmetry or Affinity have harder compound but don't give good handling.
www.tirerack.com has an extensive database on tires, email them for advice for a good compromise betweed handling and wear.