You do not have to file a return for New Jersey unless their payroll department accidentally withheld taxes for their state instead of your resident state of Pennsylvania. What matters is where you earned the income - not where your employer is located. In your case, if they only withheld PA state income taxes, you do not have to file a NJ return.
For more information, please see Do I need to file a nonresident return for an out-of-state employer?.
Secondly, you should file your unemployment claim with the state where you worked, which would be Pennsylvania. Per the Pennsylvania Office of Unemployment Compensation, you will need to file an interstate claim in another state only if you worked in a different state.
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