While the "Father" is ultimately the last enemy boss in Fullmetal Alchemist, all the Homunculus are his close soldiers. Keeping up with the RPG analogy, they are the mid-level boss, if you will. They are the ones that Edward and friends have to go through before facing the "Father".
Homunculus themselves are seven beings that represent seven sins, or traits, of humans. Each represents the particular traits that "Father" has shed from himself in order to make him a perfect, emotion-less being. They are highly important characters to the story, and this is what happened to each of them at the end of the Fullmetal Alchemist.
Lust
When they were pursuing Barry the Butcher, Colonel Mustang and Second Lieutenant Jean Havoc stumble across Lust and begin to fight her. Colonel Mustang triggers a closed-room explosion that can evaporate ordinary people, and yet she simply regenerates out of thin air. Not only that, she even manages to stab both the Colonel and Havoc with her blade-like fingers.
Their big break comes when Lust thinks that she has killed the colonel and leisurely fights against Alphonse Elric and Lt. Hawkeye. That is when Mustang suddenly attacked him from behind. He keeps on blasting her with numerous intense explosions to the point she can no longer regenerate and simply turn to dust.
Gluttony
As a homunculus, Gluttony can eat anything he wants. However, the one characteristic that makes him dangerous is his detection ability. Once he catches a whiff of something, he will be able to find it no matter where it is in the world. That being said, he is not a good fighter, and he always dies multiple times whenever he goes against strong opponents.
That is precisely the case when they fight against the Elric brothers, Van Hohenheim, the Chimeras, and Ling Yao and his companion. Both of them sustain a heavy damage, but Gluttony is nearly at the end of his regenerative limit. Feeling cornered and annoyed, Pride kills and swallows Gluttony. This allowed him to use Gluttony's keen sense of smell, but he is also plagued with his insatiable hunger.
Envy
Envy's main power is his shape-shifting ability. That being said, he is often stuck in a situation where he has to fight against multiple people. In that situation, Envy will usually revert to his true form, which is a giant lizard-like beast with human limbs and faces dangling from all over his body.
His last fight happened underneath the capital city. The whole gang is there, but the one who gives Envy the hardest time is none other than the Flame Alchemist, Roy Mustang. Enraged by the fact that Envy is the one who killed his best Friend, Maes Hughes, Mustang goes berserk on him. Combining pinpoint blast to the eye and scorching the feet with a sea of flames at the same time. However, in the end, Envy chooses to take out his Philosopher Stone and end his own life, rather than being killed or pitied by the humans that he despises so much.
Sloth
While the fight against Envy happening underneath the capital, a brawl against Sloth happening above the ground. Sloth received an order to kill "The Northern Wall of Briggs" Major General Olivier Armstrong, who happens to be with her brother, "The Strong Arm Alchemist" Major Alex Armstrong.
Both of them manage to handle Sloth at first, but unfortunately, Sloth's speed and durability proved to be a massive challenge. That is when the Elric brothers' teacher, Izumi Curtis, and her husband come to help. All four of them working together can finally kill Sloth faster than his regeneration could keep up. Sloth ends up falling on his back, smiling because he can finally rest, and dissipate into thin air.
Wrath
The homunculus named Wrath is actually the Führer of Amestris, King Bradley. Before becoming a homunculus, he was actually a regular human being. A philosopher stone from "Father" imbued into his body turns him into a super-soldier with enhanced strength, speed, reflexes, and most importantly, ultra sharp eyesight. However, unlike his sibling, he ages just like a regular human being.
His final fight began at the front of the presidential palace. He fought against the soldier from Briggs and Ling Yao/Greed and his companion from Xing. The fight is fairly one-sided, but the sacrificial attacks from both Captain Buccaneer from Brigs and old man Fu from Xing manage to land a fatal wound on his body. He then moves on to duel against Scar in the lower level of the palace. It's an incredibly difficult fight for both, but Scar finally manages to decapitate both of Wrath's hands, until he finally dies due to his many injuries.
Pride
Pride is the first homunculus, and he is a bit tricky to fight. His main body is that of Selim Bradley, King Bradley's 5-year-old son, but his other form is that of a shadow that can see, talk, eat, cut, and even hold or strangle his opponent.
In this final fight, however, Pride is severely wounded due to having to force Roy Mustang into committing Human Transmutation with him as the medium. As such, he is considerably weakened. That's why when he fights against Edward Elric, the Fullmetal Alchemist manages to invade his consciousness and force his true self out, which is a tiny baby. After that, just like the other Homunculus, his body begins to disintegrate.
Greed
Greed is the last Homunculus to leave the earth. Unlike his siblings, Greed has always been following his own whim and not the Father's will. After he was injected into Ling Yao's body, he learns to accept humans and even enjoy their company.
Greed has the ability to carbonize his skin, which provides resistance against all kinds of physical attacks. In the final fight against the Father, Greed purposely attacks him knowing that he will absorb Greed because he needs the Philosopher Stone. Once he is inside, Greed begins to carbonize Father's limbs. But instead of making it stronger, he makes it brittle to the point of falling apart. Enraged, Father eliminates Greed from within. And that marks the end of the Homunculus.