***This answer is for general information purposes only, does not constitute an attorney-client relationship, and is not meant to be a substitute for consulting with an attorney.***
The first thing you must do is post bail. This way you will not get arrrested in the even you get stopped by police. Second, once you pay bail, your tickets will be scheduled for a court date. In court you can either plead guilty or not guilty. If you plead not guilty, you'll be permitted to plea bargain with the prosecutor to either dismiss some or all of your tickets. If you don't like what the prosecutor is offering you can go to trial.
This is a practical concern because you want to resolve your traffic fines but if you go to the Court to do so you might get arrested for the traffic fines you have yet to pay, caught between the proverbial rock and the hard place. The answer depends on the kind of tickets you have. Most courts in NJ will allow you to pay your outstanding ticket in addition to the warrant fee with whats called a "bail waiver." If you don't mind eating the points, contact the Court and explain you want to resolve it. They can send you the bail waiver which you sign and send back with the payment. What the bail waiver is acknowledging is that you got the ticket, you didn't pay it, you want to pay it, your guilty, you don't want a trial and apply this money to pay off the ticket and warrant fee. That will resolve the matter. This saves you a trip to Court and the possibility of getting arrested for the other tickets you didn't pay.
Do the same thing to each Court and your matters are resolved. Again you have to determine whether you want to accept the points associated with the tickets (I'm assuming that you have moving violations which carry points). You might determine that it would make sense to actually appear in Court and take your chances with the Prosecutor. When you contact the Court by phone try to feel them out to see if it make sense to appear. Some Courts are happy to have you arrested, some are more lenient and understand you're just trying to get out from under your tickets.
Of course, if you can afford it, it makes a lot of sense to hire an attorney. You can avert most of your concerns and likely avoid most of the point consequence.
Good luck and be safe!