Probably the second most famous immortal villain at DC Comics (and probably the most famous whose only hook really is his immortality), Vandal Savage is one of the oldest members of DC's Immortals group, as he gained his immortality when he was a cave man 52,000 years ago.
He's essentially seen it all, and that plays into his whole demeanor, as he is a man who has taken part in all of mankind's greatest achievements, so it is hard to put much of a dent in his focus. He has taken on a higher profile recently when he became the main villain of the first season of the Legends of Tomorrow TV series.
When Carter Hall was introduced back in the Golden Age, the fact that he and his girlfriend were both reincarnated people from ancient Egypt was literally the hook behind his character, but then it was mostly abandoned in the years since in favor of more traditional superhero stories. This remained the case until JSA was relaunched in the late 1990s, when the new Hawkgirl debuted, a young woman named Kendra Saunders who did not understand that she was the latest incarnation of Hawkgirl. It was only when she became a superhero and, of course, met the latest incarnation of Hawkman that her destiny really began to solidify.
Their relationship was a big part of the Legends of the Tomorrow TV series (where she and Vandal Savage have a distinct connection), but in the current DC Universe (where Kendra has not yet popped up on the main DC Earth, although a version of Kendra was on Earth 2 as Hawkgirl), Kendra is someone who has already gone through her Hawkgirl period and is now moved on to become Lady Blackhawk, the head of the Blackhawks. She is much more in control of her destiny in the current DC Universe than she ever has been before. It really serves the character well.
Abel, like his brother Cain, became the host of one of DC's two major horror magazine (Cain had House of Mystery and Abel got House of Secrets). Cain was a good-natured soul, which contrasted with his vicious brother, who continually, well, killed Abel! Of course, Abel would then just come right back and their twisted game of brotherly "love" would continue for eternity.
Like the other classic horror hosts, Abel's main function is as comic relief to contrast against the dark stories that he then introduces. Abel received a cute pet gargoyle named Goldie during Neil Gaiman's Sandman run.
RA'S AL GHUL
Probably the most famous of DC's immortal characters, Ra's Al Ghul at least has a bit more going on for him as a character than his immortality, as he is one of Batman's greatest foes, which is saying a lot since Batman has such an amazing Rogues Gallery. Ra's is often defined as an eco-terrorist, but that basically means that he wants to wipe out most of humanity to return Earth to its previous population state. In fact, for someone who ostensibly loves the environment, a whole lot of Ra's plots involve things that could damage the environment as well as the human population.
Ra's uses the magical waters of the Lazarus Put to keep him alive for hundreds of years (which, as Dark Nights: Metal #2 notes, makes him far younger than the other immortals, who have generally been alive for thousands of years). His daughter, Talia, has often betrayed him in favor of Batman. Ra's is actually grandfather to Batman's son, Damian Wayne.
We believe that the final visible member of the group is a revamped Baron Winters. Baron Winters was a man of great mystery, so it is unclear exactly how old he is, but he certainly appears to be quite old (he seems as though he has a connection to the Biblical Adam and Eve).
Winters ran a group of people unofficially known as "Night Force," as Winters would put together a team with different people for each mission depending on their suitability for the mission. Winters couldn't go on the missions himself because he was trapped within his magical house. It appears as though that's changed since DC Rebirth.
There were also three obscured figure, but we're pretty sure that we know who they are.