Lived in NJ for 10 mo, moved to PA for 2 mo, still back to NJ weekend, worked in DE. Do I need to fill tax for PA? in W2, part salary was put in PA, no state income tax

If you can claim being a NJ resident for 2018 your filing will be simpler.  This is because NJ and PA are reciprocal states, so income earned in PA would be taxed only in NJ anyways.  The idea is you would be able to eliminate the PA return altogether if no PA tax was withheld.  You would file a DE nonresident return for the income earned in DE and a NJ resident return.  NJ (not PA) would tax the income earned in DE, but would give you a credit for the taxes paid to DE on that income (you prepare the DE return first so the credit transfers over).  

Otherwise it is more complicated:  you would still file a DE nonresident return, and part-year returns to NJ (on exclusive NJ income), and a part-year return for PA (which would also be taxing the DE income), and you would claim a credit for the DE taxes on the PA part-year return).

That's why, if you can justifiably say you did not move to PA (for tax purposes) until January 1, your 2018 state tax returns will be a little easier, because you will eliminate one of them.