Do the stars in irregular galaxies orbit anything? Do the stars of irregular galaxies (such as the Magellanic clouds) orbit a more precise point or are they just, I don't know, flying around? If they orbit, how stable would such orbits be, considering the overlapping of many different stellar orbits without any main ecliptic? This post doesn't mention irregular galaxies.
Although the answer you link to doesn't mention irregulars, the answer applies to those as well: Star move around in the common gravitational potential created by everything in the galaxy, i.e. gas, stars, and, in particular, dark matter.
This potential has a center, but there isn't necessarily anything exactly at this center. The stars then move on elliptical orbits around the center, but are perturbed by local irregularities.
In spirals and elliptical, the potential is rather symmetric, whereas in irregulars it is quite… irregular. That means that, if you were to take two images of a galaxy, separated by a period of order the dynamical time scale ($t_\mathrm{dyn} \sim \sqrt{R^3/GM} \sim 100$ million years), a spiral and an elliptical would look more or less the same, while the irregular would probably have changed its shape notably.