Active duty in VA living out in town,HOR is NJ.How do I file as a non resident of NJ? Was told by NJ to file as nonresident. But Turbotax considers me a full resident.

You are correct that New Jersey will consider you a non-resident.  See below for steps to go through to change the status within your New Jersey return.

If you stated in your My Info section for your federal return that you were a resident of New Jersey, plus selected that you were active duty military, then go ahead and start the New Jersey state return, even though it says it is for a RESIDENT.

Continue through the New Jersey return screens, even selecting county of residence (for your HOR) and municipality, until you are brought to a screen that is titled "Other Situations that May Apply to You" and then check the box for "I need to verify my main form or residency section."  See the sample screenshot attached. 

On the next screen you will be asked about your active duty military status and questions to determine whether you qualify for the non-residency status.  Be sure to check two boxes:  1) that you paid for and maintained a residence outside of NJ (and then list the state) and 2) that you did not spend more than 30 days in New Jersey in 2018.  See the sample screenshot below.  This will then change your tax status for New Jersey to Non-Resident.