The orbit of the Sun around the Galaxy is quite complicated, because unlike the solar system, the mass is not completely concentrated at the centre. So, in addition to the roughly circular 230 million year orbit in the plane of the Galaxy, there are superimposed motions in and out of the plane and towards and away from the Galactic centre. These roughly sinusoidal additional motions, called epicycles, do not have large amplitudes - a few hundred light years - and take about 70 million and 160 million years respectively.
The Sun does not systematically orbit any other Galactic structures or stars (see the flagged potential duplicates for more details - there is no evidence for any binary companion to the Sun larger than a few Jupiter masses) and is unlikely to do so in the forseeable future. The space between the stars in our Galaxy is large enough that they are essentially non-interacting.
The Galaxy itself is in motion with respect to the galaxies around it. The nearest tens of galaxies form the local group and probably have complicated orbits within their summed gravitational potential. These orbits cannot be precisely determined, because although we can measure line of sight velocities using the Doppler effect, the tangential motions require extraordinarily accurate position data over many years. These are now becoming available - for instance we know our Galaxy and M31 will collide in around 4 billion years.
Further afield, the local group is part of a larger galaxy aggregate, called the Virgo supercluster, but here, determining an orbit is impossible.
Even further, large galaxy clusters are arranged into a web of larger superclusters, voids and filaments that are all in motion with respect to each other.
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