One problem related to steering wheel vibrate has been reported for the 2007 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2007 Honda Odyssey based on all problems reported for the 2007 Odyssey.
I own a 2007 Honda Odyssey and have been having problems with my brakes for some time. They feel very soft and "spongy" when I step on them; my foot sinks all the way to the floor. There have been numerous instances where I have almost hit another vehicle because the brakes do not respond. The brakes also grind very hard and sound very loud when I come to a complete stop at the bottom of a hill. Also, when I try to stop or slow the van when traveling at high speeds (such as highway driving), my steering wheel vibrates violently. I have taken the van to the mechanic and have been told that my brake pads are fine (50% front, 60% rear), but that my rotors have worn prematurely. I also had problems with my power steering--I took the van in for service because I had a difficult time maneuvering the van in tight situations (parking)--it turns out that my power steering pump was not operating and needed to be replaced (at 36,267 miles)--267 miles over the Honda new car warranty.