Is it nice-ish stuff that you just don't want or have a need for, or is it junk that no one would want?

If the former, then an estate sale might be an option (or they might be able to point you to the someone who runs a thrift/antiques shop that can help with a clean out at no cost.) We do a lot of antiquing at estate sales, and not all of the "hosts" have houses full of swanky art and furniture. Especially if you don't care about getting any profits yourself, this may be an easy option, because you don't have to necessarily price stuff and organize it like at a yard sale. Sometimes you'll see a sale listed as a "diggers paradise", which basically means anything left in the house is fair game. A list of local estate sale companies can be found here: https://www.estatesales.net/companies/NJ/Northern-New-Jersey

If it's total junk that no one would want, then a paid clean out service is probably your best bet. You can look on Craigslist for "eviction clean outs" and find local people who do it, which is usually cheaper than 1-800-got-junk.