Abu has a huge passion for all of the morals and beliefs that he has, no matter how ridiculous some of them may be. He acts very hyper often and freaks out easily. He's very obsessed when it comes to girls he likes, starting with Rita at the start of the series, and then again with Strawberry later on in the series. Although he's usually nice when people aren't mean to him, he can be very cruel at times, like thinking to himself that he wouldn't really care if he caused Dan to have mental damage at the end of the first part of the Shadow saga, which results in disastrous consequences.
During his training in the Prologue episode, he eventually learns to form blue chains of energy from his paws to grab a tree branch and bring himself up with it. This is his energy chain ability, his most unique ability of all. He uses it to reach places, throw hams, reel hams in, block certain attacks, and more. After the Strawberry saga, he can more easily change the chains to different shapes like huge battle axes of energy. It's then explained that this is because of how much he has become used to changing the form of Shadow energy, especially during the last episode of the Judgement saga.
Besides that, he's a fast and swift ham with a martial artist type of fighting style. Throughout the series he has transformed into "Hyper Abu," "Shadow Abu," and, when fusing with Sauce while Abu's in Shadow mode, "Shadow Saubu."
Involvement in the Prologue
In the start of the series, the Prologue, Abu (nameless at the time) lives with his human owner that is also named Abu. However, his human owner Abu then leaves to move out to a martial artist dojo, accidentally leaving Abu (the ham) behind. Abu ham then chases human Abu's car, but ends up not making it. He then wanders around and finds a town of ham clubhouses. That's when he finds the Hamtopia clubhouse. He first introduces himself as Martial Artist Ham. He instantly gets a crush on Rita and freaks out about it, but the members there just find him annoying.
Abu (as "Martial Artist Ham") wanders outside again and finds the Hamtaro clubhouse being taken over by the Punk Hams. Abu loses to them, so he trains outside in the forest, eventually getting his clothes, blue eyes, and his abilities. He fights Max the Punk Ham in the slide room, and this time he wins. When asked who he is, after all of the training Abu went through and becoming who he is now, he thinks of his martial artist owner Abu that he admires, and decides to call himself Abu after his owner. It's then that he joins the Hamtopia clubhouse.
Involvement in the Rivals Saga
In the first part of the Rivals saga, Abu's rival is Max the Punk Ham. Abu trains the Hamtaro hams and Hamtopia hams to be able to fight, helping some of them learn their abilities. In the last part of the saga, the hams work together by holding their paws, giving their spirit and energy to Abu, to have Abu become Hyper Abu during his fight with the main shadow ham. Through this method, Abu and the others end up winning the battle finally.
Involvement in the Shadow Saga
In the first part of the Shadow saga, he creates an online game called RPG World on a laptop and resorts to pretending to be a human girl (who looks like Marle from Chrono Trigger, since you can be her in the game) in an effort to make the game become popular. The plan is ridiculously successful, but due to all the guys constantly asking him to be their girlfriend, he has a ham called Dan be his boyfriend. Abu doesn't really care about him much though, and is seen thinking cruel remarks about him all the time. When the players meet up, causing Dan to find out that Abu's a guy, it causes Dan to freak out and eventually become Sikeeh who has a lot of hatred (and hidden love) for Abu. Eventually Abu weakens and distracts Sikeeh until Sauce is able to sneak up and kill him.
In the second part of the Shadow saga, Abu finally gets Rita to be his ham (girlfriend) with help from Sauce. Rita and Abu create a new clubhouse called Ham Ham Rivals. Eventually, there might be a two episode mini-story about a game that Abu makes for Rita, called Rita's Adventure.
Later, Sauce persuades Rita to break up with Abu and to be Sauce's girlfriend instead. A new Punk Ham appears that keeps hanging around Abu, saying crazy stuff to him. It ends up that this new Punk Ham was all in Abu's head and was actually an illusion of his.
Eventually, Abu transforms into Shadow Abu (a power that Sikeeh also had in the first part of the Shadow saga,) and chases after Rita while fighting hams in his way. When he finally makes it to Rita and Sauce ends up sitting high above them taunting Abu, Abu transforms into a monstrous Shadow creature and shoots a large blast of Shadow energy at Sauce (which it turns out that Sauce avoided getting hit too much by it.)
Abu turns back to Shadow Abu, and all of his Shadow energy makes Rita become a dark Shadow-like form herself. In this form of hers, her whiskers vibrate a lot, and she can move really fast to avoid all of Shadow Abu's angry attacks at her. In the end, Abu fails at doing anything and just goes back to his room.
Involvement in the Ham Ham Kingdom Saga
Abu's plan of flirting with as many girls as he can ends up getting Nora to get a crush on Abu. During this saga, costumed ham hero Sima Matt becomes Abu's best friend as a replacement for Sauce. Later, Sonar becomes Abu's ham (girlfriend.) In the end, Rita becomes single again, which causes Abu to dump Sonar as quickly as he possibly can upon hearing the news and talk to Rita once more. During the talk, he says how he just wants Rita to be with someone like Sima Matt and suggested her to be with him, saying that he's a good guy who wouldn't end up doing perverted things with her and wouldn't betray him.
Between the Ham Ham Kingdom Saga and Human Saga
Yeah, I don't know what to call these group of episodes right now. Anyways, later, Rita does end up with Matt, and he ends up doing perverted stuff with her, and he ends up betraying Abu and everyone at Ham Ham Rivals by using Rita's power over the place to name himself God and calls the members his minions. He tells Abu how he's the worst ham in the world, even though back when they were friends he made a special gift for Abu that told him to never change because of how good he is. Eventually Abu fights Matt, but even as Shadow Abu, Matt easily dodges all of his attacks.
Involvement in the Bad Future Saga
Eventually becoming Shadow Abu, and then eventually fusing with Sauce to become Shadow Saubu, Abu fights Sikeeh.
Involvement in the Human Saga
Nothing very plot worthy happens in this saga until the end. Abu (in human form, since everyone has been turned into a human form for this saga from a Shadow ham's spell) ends up being saved by a group of cyborgs by human Abu (human Abu as in his owner from the start of the series) and his pals, the ones from the Abu's Quest games. They have a friendly fight back at human Abu's dojo during an opening to an episode (the opening being "Yura Yura") in which human Abu ends up winning, though it doesn't matter much since the fight was just for fun.
Involvement in the Movie
Abu fights a Shadow ham that has the ability to shapeshift into the ham that the Shadow ham is fighting with's most loved ham in order to make it harder for the ham the Shadow ham is fighting to fight, but when the Shadow ham shapeshifts into Rita, it just makes Abu turn into Shadow Abu and fight better as Faint by Linkin Park plays. In a later fight, Abu is defeated, but saved by Sikeeh. In the last fight, Abu teams up with Sauce and Sikeeh. I haven't planned much else of the movie yet, so I don't know any other details yet.