Check your rear subframe bushings. They may be worn. All that power you are putting down is only worsening the problem. You can alleviate the problem by compressing the subframe bushings with the following:
http://www.specialtyz.com/subspacers.htm
Install instructions are on this page:
http://www.capitalzoftexas.com/techtips/
Don't let the 300ZX info on the page fool you....240SX's have the same setup and follow the same install procedure.
Anyhow hope this helps.
ID