It's not unusual to see migrating stripers this late in the season when conditions are like this. Ocean temps along the NJ shore are still in the mid 40s. A few years ago there were still fish into mid Feb but - honestly - this isn't typical. Moreover, many of these late run fish after the beginning of the new year tend to be off the beach under blueback herring. Yes, they'll be catchable from the beach if you time it right but this late run fishing tends to be a boat game. The fish will leave eventually - sometimes this doesn't completely happen until March by which time the bass are gone (except for the remnant power plant fish in bays and rivers).
Unless you live close by, I wouldn't make a long drive to the shore.
If you're close and the weather is nice....what the heck? It's always nice to walk the beach. And catching a fly rod striper in mid winter would be pretty cool and definitely worth some bragging rights IMO.