My son is a college student in PA, his permanent residence is DE. His employer put his PA address on my W2, should he file PA return as a resident or non-resident?

He would file a PA return as a non resident and then a DE return as a resident.  There is not really a difference other than he will then take a credit for taxes paid to PA on his DE return.  You will attach Schedule NRH to his return as a non resident. 

In general, your home state will tax all in come from all sources.  What you will do is you will file a nonresident return for the states that you do not reside in, but you visit for work and earn money in.  When you file, you will fille out your nonresident states first.  Then you will fill out your resident state, claiming a credit for taxes paid to the nonresident states on your home state return.  You may or may not still end up owing money to your resident state depending on whether or not their tax rate is higher or lower than your nonresident state.  If the non resident state had a higher tax rate than your resident state, your credit will be limited to the amount of tax you would have paid to your resident state.  They will not give you a refund of the taxes you paid to the nonresident state. 

Multiple States

File Non Resident State Return