My tenant signed a one year lease 18 months ago. Two months later, his girlfriend moved in with her kids (not on the lease). 15 months ago, he was incarcerated for internet fraud. "They" are now behind $8K+ in rents and penalties. With the lease clearly expired and he no longer in residence, do I need to go through a lengthy eviction process or can I have her (squatter?) locked out with a 30 day notice?

She's not a squatter - she's a resident. She needs to be evicted.

He signed a one year lease 18 months ago so the lease has expired (not that it matters much)?

Correct, she is a resident with all the rights of a tenant. You were apparently aware of her moving in and did not take action so she became your tenant as well.

However, this should not be that lengthy an eviction. If they owe more than $8K I doubt if they will be able to come up with the money. So you serve them with a pay or quit notice. I think NJ uses a 3 day notice period for pay or quit. Since its unlikely they will do either, you will probably need to go to court for an eviction order. However, that may give them time to find someplace else.

My question to you is why did you let it get this far? As soon as they fell behind you should have given a pay or quit notice.

Scott is right - it's a 3 day notice to pay or quit: "The notice for Failure to Pay Rent, or Substantial Lease Violation is three days.

".. . A demand that said tenant remove from said premises within three days from the service of such notice. The notice shall specify the cause of the termination of the tenancy, and shall be served either personally upon the tenant or such person in possession by giving him a copy thereof, or by leaving a copy thereof at his usual place of abode with some member of his family above the age of 14 years."
".. . It shall be shown to the satisfaction of the court by due proof that the notice herein required has been given."

http://rhol.org/csu/evictions/New%20Jersey/NewJerseySteps.htm

Yes we should have done the quit a long time ago. Unfortunately, we are "nice" landlords as my social worker wife would say. We have a few properties and have never been burned before, even though it has taken time for folks to catch up. Just wanted to make sure she has same rights as a tenant.