Ask Mr. Smarty Plants

You have a real problem, and we cannot even excuse it by saying it is a non-native plant. Phragmites australis (Common reed) is native to North America and very invasive. There are introduced, non-native forms of it also, but both the native and non-native forms have the same habitats, From our webpage on the native plant (which read by following the above link),  this paragraph:

"This tall and striking plant rarely produces seed but spreads vigorously by underground stems (rhizomes), often running over the surface of the ground for 17-34 (5.1-10.2 m). It can form dense stands that exclude all other wetland species. It is the dominant vegetation of the still extant Hackensack Meadows of New Jersey where it filters pollutants from the greater New York-New Jersey metropolitan area. While this role may appear beneficial, it has no doubt out competed the native vegetation that would ordinarily serve this purpose."

According to this USDA Plant Profile Map, the common reed is native to New Jersey and growing in Ocean County. In fact, it grows natively in all of the lower 48 states, as well as most areas in Canada. We will try to find some research on eliminating this plant from your property, but we should warn you that with the underground rhizomes, it is very resistant to extermination, and obviously there will be other populations of it nearby that will simply move into the space left if you are successful in destroying the plants on your property.

From invasiveplants.net, we found this article on Phragmites, which doesn't tell you much you don't already know.

Another article from the Plant Conservation Alliance Alien Plant Working Group LEAST WANTED on Common Reed has some Management Procedures, but as we pointed out before, neighboring plants will quickly fill the gap. It would appear that a joint effort of agencies and property owners is your best chance for success. We would suggest you contact the Rutgers University Cooperative Extension Office for Ocean County to inquire about the possibility of such an undertaking. There is contact information on that site for the various departments and services.