On September 9, 1976, they fought Doc Toxic.
In late April 1982, they were in combat with the Micron army who were attempting to fire a weapon into the atomic world, which would have vaporized several large Western U.S. states. They managed to foil the sub atomic race's plans with Solid absorbing most of the impact. They rematerialized to full size in an Astro City apartment building, which ended up collapsing.
The Experimentals possess the ability to transmute matter, transitioning it from one of the four states to another, though the precise sorts of transitions they are capable of differ from member to member. For example, solid can transmute energy or gas into solid mass -- which he can add to his own mass, bolstering his size.
In addition, their bodies possess the characteristic traits of their respective states of matter. Liquid is fluid-like and malleable, able to elongate limbs and such. Vapor and Ener-Jeannie can both fly, and the latter fires energy blasts.
Brian Kinney mentions that, as part of their effort to pacify the world's heroes, the Enelsians confiscated the Experimentals' stasis pods in 1997. Though the quartet is seemingly out of action in the modern day, this incident would seem to suggest they are at least still alive in some form. Perhaps they're being kept in stasis permanently or for a long duration.
According to the backmatter of the first Dark Age trade paperback, there is a mysterious fifth Experimental. As yet, next to nothing is known about them or their nature.