There is a loud, squeaky, high-pitched noise when driving, but it stops when braking.
From the description provided, it appears that your Honda Odyssey may be experiencing worn out brake components. While it may sound strange that the noise you are hearing disappears when the brakes are applied, it does not mean the noise has gone away. That noise actually grows louder but we are unable to hear the high pitched frequency when the brakes apply pressure to the brake pads.
Due to this noise being so specialized, at this point I feel it is best to recommend enlisting the help of a certified mechanic to come over and inspect your Honda’s braking system. They will perform a test drive to confirm what the noise question in person. This involves removing the wheels and carefully inspecting all of the braking system components to determine if your Odyssey needs to have its brakes cleaned and adjusted, or if it is time to have your brake pads replaced.
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