Q: what can cause a constant rattling noise when the vehicle travels over bumpy road? on 2000 Honda Odyssey

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Both front strut assemblies and both rear shocks have been replaced. In addition, both sway bar links and control arm bushings have been replaced too.
(2) Answers
A good physical inspection of your steering and suspension should reveal where a noise is occurring.

My guess would be that you may have a strut mount with a worn bearing causing some noise. Just a guess.
Very likely that a strut mount is bad. If the strut mounts have been replaced, I have seen the actual spring seat break and cause noise as well. May have to disassembly the struts in order to pinpoint the location and cause of the noise