Good questions. There's a lot to cover here. The short answer is: "Yes, file NJ-1040 resident and NC D-400 resident w/ Schedule PN tax returns. Possibly NJ-1040NR as well."
New Jersey states:
"Part-Year Residents. There is no part-year resident return. You may have to file both Form NJ-1040 to report income you received for the part of the year you were a resident and Form NJ-1040NR if you had income from New Jersey sources for the part of the year you were a nonresident."
The NJ filing threshold is $10,000 ($20,000 for head of household or married filing jointly). You would need to file the NJ non-resident form if you received, say, a NJ bank 1099-INT interest form for interest earned after you left NJ.
North Carolina states:
"For tax year 2018, a North Carolina tax return is required if your
federal gross income exceeds the amount listed for your filing status
shown below: ... $8,750 single, $17.500 married filing jointly, $14,000 head of household."
NC income tax is 5.499% of your total taxable income multiplied by the percentage of that income attributable to NC residency.
As to your second question, how to go about filing depends on both your income types and levels and your comfort with do-it-yourself methods. Assuming your income is relatively simple, say wages and, perhaps, bank interest, you can certainly use the TurboTax Free Edition to do your Federal income tax return.
For the two (or three) state returns, let me know more details of the types of income and credits (e.g. out of pocket education expenses) and whether you are at least age 24 and older. And, of course, how comfortable you are with trying the do-it-yourself approach first. State income tax returns are generally easy as they are based on numbers copied from your federal return, tweaked with a few state-specific adjustments. In any event, you will need to split your income into two columns, one for NJ and one for NC, in order to fill out those returns.
