All elliptical galaxies have n between 0 and 7. Irregular galaxies have no obvious spiral or elliptical structure. It is thought that many irregulars were once spiral or elliptical, but that a close encounter with a larger galaxy disrupted the organization of hte material by gravitational forces. I's are resolvable into individual stars, and Irr II's are not. Not all galaxies are easily classified.
Quasars are the bright, superluminal cores of very distant active galaxies.
These galaxies are so distant in fact, that the quasars look like stars in most images. However, their redshifts are so high that we know that they can not be stars. These quasars are moving away from us at extremely high velocities. The relationship between galaxy types is not clear. Because there is little evidence of star formation in elliptical galaxies, and because they seem to have extremely small angular momentum, it was thought that perhaps elliptical galaxies are much older than spirals.