You have not clearly stated where you actually did the work, but that's what really matters. If you worked only in New Jersey for clients or employers in other states, all of your income was earned for working in New Jersey and you file only a New Jersey state tax return. It doesn't matter where the client or employer is located. It also doesn't matter where you live. What matters is where you did the work.
On the other hand, if you went to other states and did some work there, you have to pay tax to each state where you worked, on the income that you earned for working in that state. That means that you have to file a nonresident tax return in each state that you worked in. (Washington state and Wyoming are exceptions, since they have no state income tax.) This is true whether you are an independent contractor or an employee. All of your income is also taxed by the state that you live in, no matter where the income is from. But you will get a credit on your New Jersey resident tax return for tax that you pay to other states.
