There may be some local deviations from intense mass clusters but basically every star orbits the centre-of-mass of the Galaxy.

Velocities can be measured in edge-on galaxies by doppler measurements, but it's tricky building up a picture of individual star movements in a 200-billion star galaxy. You either have to settle for averages over large numbers of stars, or ping only a few stars and hope that they're representative of the whole.

There are distance effects here too - one can generally only measure individual stars in relatively near-by galaxies. Pretty soon, everything fades into a blur in the distance, even for Hubble.

Also, except for the case noted of Sgr A*, it's difficult on a human timescale to see the curvature of the orbits - we only see an instantaneous vector tangent to the orbit and have to reconstruct the rest by a bit of guesswork.

You may be best looking at simulation models of galaxy dynamics, rather than trying to measure a real one in detail...