Not really sure if it's a "Private" Party, rather than just tickets into the park. The entire park is open for day guests until 1am and Disneyland side until 2am. Most years the radio stations have dance areas (DJ's) setup in different areas in DCA, the fireworks over the lagoon are pretty cool to since they are so close to you (if they are the same this year). Disneyland has the big Main Street events and more near Small World as well.
They may have a small sectioned off area for the Power 106 "VIPs", but thats about as private as it will be, since the park is open. But hey is New Years Eve, unless you already have other major plans I would go.