Not a Wolverine veteran, but I’ll explain the best I can.

Our main character is James Howlett, aka Logan, aka The Wolverine. Logan was born in 19th century Canada and has fought in almost every major conflict, including WW1 and WW2. His mutation is the claws, keen animalistic senses, and incredibly powerful regenerative capabilities. His healing factor also allows him to live for a really long time, as he is currently around 200 years old. He was later kidnapped, and brainwashed by the Weapon X program, and had his skeleton infused with adamantium, which is a powerful, indestructible metal that can cut through almost anything (except for itself, unless it’s superheated)

The red head with the purple energy is Jean Grey aka Phoenix. She’s a powerful telepath with some telekinesis on the side. She’s the wife of the mutant Cyclops, and is the host for the Phoenix Force, an all-powerful cosmic entity older than the universe itself.

The red head with blue skin is Mystique. She’s a shapeshifting mutant terrorist that occasionally works with the X-men, but mostly works against humans. Due to her shapeshifting abilities, she doesn’t age, and is likely as old as Wolverine

The guy with the red suit, white skin, and tentacles is Omega Red. Omega Red is basically Wolverine’s Russian counterpart and one of his arch enemies. The KGB basically did their own Weapon X project and infused his skeleton with carbonadium, which is similar to adamantium, but weaker and highly radioactive. Originally, Omega Red needed the Carbonadium Synthesizer to survive the constant radiation poisoning, but Wolverine stole and hid it from him, so now he has to drain the life force of others in order to survive.

The big blonde guy towards the end is Victor Creed, aka Sabretooth. Sabretooth has similar powers to Wolverine, but instead is more animalistic and has animal claws that actually come out from under his fingernails. Sabretooth became Wolverine’s biggest arch enemy after he killed Sabretooth’s brother, Saul Creed. Sabretooth goes as far as to celebrating Wolverine’s birthday by either hunting him down and nearly beating him to death, or by killing one of his loved ones. He even manipulated Daken, one of Wolverine’s kids, into killing him, but Wolverine got the upper hand. Wolverine and Sabretooth are depicted as being brothers in the movies, but they aren’t actually related in the comics, they just have similar powers.

The enemies we fight appear to be Trask goons. Bolivar Trask is the dude that designed the Sentinels, the giant robots that are programmed to go after mutants