In total we have measured around 50 stellar orbits around Sgr A*. The stars on these orbits are commonly referred to as the "S-stars" (Schödel et al. 2002, Eisenhauer et al. 2005, Gillessen et al. 2009, Gillessen et al. 2017). The following figure shows how the projections of the orbits onto the plane of the sky looks like.
Actually, we have measured the orbits in three dimensions, such that we can build a full 3D model of the motions of the S-stars:
The visual impression of this stellar system is that the inner orbits follow no apparent order, but a bit further out, there are a few stars that orbit on similar planes. The randomness of the inner orbits holds in two senses: In the distribution of how the individual planes are oriented, and how the eccentricities are distributed:
The eccentricity distribution of both early- and late-type stars is compatible with a thermal distribution, n(e) de ~ e de. Taken together with the randomly oriented orbits, the stellar system appears to be dynamically relaxed. This means in other words that the stellar motions do not carry information about how stars came to reside so close to the black hole.