It sounds like you may have a worn rear strut or rear strut mount bushing. According to the RepairPal estimate page, (http://repairpal.com/estimator) 1 rear strut replacement runs from $218-$318 and the mount will only add another $25 or so dollars. It is recommended to do both sides at once.
There are various reasons why suspensions are noisy. Some 06 Accords have an issue with broken sway bar links. In cases of noises it's always best to have a good visual inspection first to see if there is anything obvious with the suspension/struts and then if nothing obvious is found then the vehicle can be diagnosed.