Sample EWR taxi fares are here. South Orange isn't on the list, but based on the distances of other destinations I'd guess it's roughly $50 + tip.

I'm not sure if Newark or Elizabeth taxis can pick up outside the cities of Newark and Elizabeth (they can only do EWR terminal pickups at the terminal(s) located in their respective city, for example). But there are almost certainly local taxi companies in South Orange or nearby that can take you to the airport. Poke around Yelp or Yahoo Local and you should be able to find a few. You can also try some of the car services listed under EWR/NJ on the page linked above. Dial7 for example will probably pick you up in South Orange.