The central parsec around the supermassive black hole in the Galactic center (GC) hosts more than 100 young and massive stars. Outside the central cusp (R 1 ) the majority of these O and Wolf-Rayet (W-R) stars reside in a main clockwise system, plus a second, less prominent disk or streamer system at large angles with respect to the main system. Here we present the results from new observations of the GC with the AO-assisted near-infrared imager NACO and the integral field spectrograph SINFONI on the ESO/VLT. These include the detection of 27 new reliably measured W-R/O stars in the central 12 and improved measurements of 63 previously detected stars, with proper motion uncertainties reduced by a factor of 4 compared to our earlier work. Based on the sample of 90 well measured W-R/O stars, we develop a detailed statistical analysis of their orbital properties and orientations. We show that half of the W-R/O stars are compatible with being members of a clockwise rotating system. The rotation axis of this system shows a strong transition from the inner to the outer regions as a function of the projected distance from Sgr A*. The main clockwise system either is either a strongly warped single disk with a thickness of about 10A?, or consists of a series of streamers with significant radial variation in their orbital planes. Eleven out of 61 clockwise moving stars have an angular separation of more than 30A? from the local angular momentum direction of the clockwise system. The mean eccentricity of the clockwise system is 0.36 A? 0.06. The distribution of the counterclockwise W-R/O star is not isotropic at the 98 confidence level. It is compatible with a coherent structure such as stellar filaments, streams, small clusters or possibly a disk in a dissolving state: 10 out of 29 counterclockwise moving W-R/O stars have an angular separation of more than 30A? from the local angular momentum direction of the counterclockwise system. The observed disk warp and the steep surface density distribution favor in situ star formation in gaseous accretion disks as the origin of the young massive stars.