I switched the rubber bushings on the sway bar and the clunking noise is now gone.
1. Use 12mm socket wrench to remove left and right bushings (4 bolts). note: you don't need to remove the whole sway bar -- the rubber bushings can be removed by themselves.
2. put the left rubber bushing (item 7 in diagram below) where the right bushing was and vice versa.
See the following link for a description and diagram of the problem. See item 7 in diagrams below. The bushings look similar to the ones pictured below, and are for attaching the sway bar to the frame.
If you want to replace worn out bushings, the part number is 52306-SCV-000 for the Honda Element. This is for years 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011. The part is also referred to as "BUSH, STABILIZER HOLDER" on some part dealer websites, for example, Sons Honda. The price is about $3 per bushing.
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