The correct plural is neither Clayface nor Clayfaces. They are collectively The Mud Pack.
First- The Clayfaces of the comics
#1- Actor Basil Karlo (obviously a combination of Bela Lugosi and Borris Karloff- though he reminds me of Vincent Price as well) was a great star. He was hired as an advisor for a remake of one his films, a horror movie titled “Clayface”. Outraged that anyone would attempt to improve on one of his films or try to outdo his performance, Karlo disguises himself as Clayface and begins killing the cast and crew. Batman and Robin stop him and he spends a decade or two in jail
#2- Matt Hagan was just a thug. Until he found a grotto with a strange pond. The “protoplasm” in the pond allowed Hagan to change his shape. Besides such things as growing claws to attack or wings to fly, Hagan could turn himself into a meteor and set things on flame ( If you doubt check out “Joker Clayface Feud” conveniently reprinted in The Greatest Joker Stories Ever Told). Hagan lost his powers after iirc 24 hours. The cave was destroyed a few times. But Hagan always found it again, or had a secret stash etc. He developed a synthetic protoplasm, but its duration was much shorter than the real thing. Hagan died in Crisis.
#3-Preston Payne- Payne was born with a disfiguring condition (was it acromegally? can’t recall). He looked rather strange. Kids shunned him. So, he turned into a typical bookworm. Eventually he became a scientist at STAR labs. Payne took blood from Hagan in hopes of isolating traces of the protoplasm. He succeedeed and injected himself in hopes of gaining metamorphic powers. It worked and Payne remade himself as a stud. He immediately went on a date. Things went fine until his face began to run like wet clay. The girl screamed. When Payne touched her, she dissolved-as did anyone else Clayface3 touched. Payne made himself an exeskeleton, to protect people and to support his gooey form. He suffered from migraines and fevers which could only be cured by dissolving other humans. All this drove him insane. He eventually fell in love with a wax mannequin. They shared a cell at Arkham Asylum for while.
#4- Lady Clay. The-evil-guy-bent-on-world-domination Lord Kobra wanted an agent with the powers of Clayface. So he experimented on an unnamed woman and got Clayface 4. Her powers are permanent. By copying the shape of other superhumans, she may copy their powers as well (The mudpack ish # ? detective comics).She has no melting touch. But, Lady Clay cannot keep any shape for long. This includes her original appearance. She must spend most of her time as a woman made of mud.
Clayface 1 got out of jail and rounded up the others, including Hagan’s remains. He tricked 3 and 4, drugged them and took samples of their blood. He forced a doctor to mix these with a bit of Hagan and inject him with the results. Karlo gained the powers of the other Clayfaces. The heroine Looker was able to increase Karlo’s dissolving touch beyond his control. He was last seen melting his way to the center of the earth.
Clayface 3 and 4 fell in love and fled Gotham. They lived as hermits for a time. But, Payne’s condition finally forced him to kill again. He melted a passing driver. It is apparently safe to touch him for a short time after he has killed, and the Clayfaces conceived-
#5- Cassius Payne. Why Cassius? “You know, Cassius Clay!” At birth, he was a gooey ball vaguely resembling a fetus. At present he looks like an ordinary boy. He has the shape changing powers of his mother, though he remains untrained in their use. He can dissolve people but this appears to be under his conscious control. Ma and Pa wanted to keep living as hermits until Abattoir, another criminal, kidnapped Cass and forced 3 and 4 to fight Batman. The Clayfaces are currently in custody.
The Animated Series-
The Clayface of Batman Adventures appears to be a mixture of the 1,2, and 3. Matt Hagan was a great actor. A car accident left him looking Phantom-Of-The-Opera/CryptKeeperish, and he thought his career was over. Roland Dagget, head of Dagget Industries, gave Hagan a substance that would allow him to mold his features at will. Hagan recieved fresh supplies of the chemical as long he carried out certain jobs for Dagget. Eventually, Hagan tried to steal the stuff, now called Renu-U . Dagget’s henchmen caught him and forcefed Hagan gallons of Renu-U. Hagan was now a huge clay thing. He could take any shape he chose, but only for brief periods. He fought Batman several times and appeared to die twice. Once he staged his own death( “Hagan said it himself, Alfred. He called it a scene. I wouldn’t be surprise if that ‘body’ they took was just an empty shell.”
In time it appeared that Hagan’s body was deteriorating. He had stolen some rare chemicals wand was about to recieve a life-saving treatment when Batman found him. A misunderstanding occurred, and they fought. Hagan fell into the ocean and seem to fall apart. But something (my guess is pollution) cured him and he returned.
I wanted to see Clayface on Batman Beyond, but AFAIK he appears in no episode and is not mentioned. A member of the Terrific Trio, resembles Clayface. But, it's a coincidence. An episode involving animated soil and dirt creatures looked promising, but turned out to be unrelated to ClayFace.
RE- Killer Croc
I believe his name is known. IIRC he was an African-American born with a condition making his skin tough and scale-like. He went on to pro-wrestling and then crime.