I Am Soup

The Green Skull, from Earth-9602. His legal name is "Alexander Luthor" and his nickname is "Lex". He's Hydra, formerly from the 1940's. and formerly married to Lois Lane! Wtf?!?!

Earth-9602 is known as the Amalgam Universe. Basically, The Marvel and DC Universes are brothers (creatively called The Brothers) who pitted their best fighters against each other. Long story short, the worlds became one because of The Living Tribunal and The Spectre. Then, a hero named Access helped disentangle the two universes, only for Doctor Strangfate to try and recreate the Amalgam Universe. Doctor Strange defeated Doctor Strangefate, but allowed the Amalgam Universe to keep existing with Access as it's overseer.

I think, at least. All of that was summarized from the Wiki.

Also, Logan Howlett is Logan Wayne, aka Dark Claw; Clark Kent is Captain America, renamed Super-Soldier; Charles Xavier is Doctor Strangefate; Hal Jordan and Tony Stark became Hal Stark, the Iron Lantern; Bruce Wayne, who isn't Batman but is an agent of S.H.E.I.L.D and an orphan; Diana Prince, who isn't Wonder Woman but is still from Themyscira; Ororo as Wonder Woman, renamed to Amazon; and Pete Ross as Spider-Boy, who has other titles/names such as Way-Cool Spider-Boy and Living Nexus of Realities and Timelines.

It's called Earth-97643. It's a branch timeline from Earth-9602, but is it's own reality. It follows Logan Wayne, the Dark Claw. It only has one comic run, Dark Claw Adventures #1, and an animated show that's a combination of Batman: The Animated Series and X-Men: The Animated Series creatively called Dark Claw: The Animated Series.

Logan Wayne's status on this wiki, btw, only lists him as "existing".

He has a relationship with a woman named Barbara Gordon Hardy, the Black Bat (formerly known as The Huntress)

Barbara Hardy is a former thief who joined S.H.E.I.L.D. She was partnered with Bruce Wayne and they fell in love. They planned to marry, and then were sent to stop a doomsday weapon. Barbara "most probably" died in the fight, and it's unknown if Bruce did. Fury is not optimistic.

bring it on!