I live in New Jersey with my girlfriend. Her name is on the lease but I pay half the rent. If she wanted to kick me out would she be able to legally?

If she is the one obligated on the lease, then she has the right to occupy the premises.  If your name is not on the lease, you do not have the "right" to occupy the premises, and therefore, if she does not want you there, I beleive she can legally ask you to leave.