Nick Fury's team! I'm also pretty iffy on Fury's history, so some stuff is pretty vague....
His Pokemon are a bit different then all the other teams because Volcarona is the only one that's actually his. Both Mewtwo and Absol are employed as official agents of SHIELD, but are seen often enough by Fury's side that most people consider them his.
Fury found Volcarona as a Larvesta early in his life before the creation of SHIELD. He had recognized the potential power within Larvesta and it took it under his wing, training it to become the fearsome Volcarona it is today.
Absol was found after its multiple appearances at areas where disasters struck. Fury, realizing that Absol was actually somehow predicting these disasters, tracks down Absol to recruit it to aid SHIELD in preventing or at least minimizing the destruction caused by the disasters. Absol, though wary at first of Fury, agrees when it realizes that people actually want its help, not chase it away. So since then, Absol has been an agent of SHIELD who leads teams when it senses impending calamities.
Fury first heard of Mewtwo when reports came in of a secret research facility destroyed by a mysterious Pokemon. He follows up on the reports and eventually tracks down Mewtwo, who had been on the run traveling the world to experience life for itself. Fury knows it is being hunted down by the people who ordered its creation, so he offers Mewtwo a safe haven in SHIELD in return for its cooperation. Mewtwo, wary, but nevertheless interested by the offer, ends up agreeing and joining Fury and becoming an agent of SHIELD.
Though neither Mewtwo nor Absol have an actual master, Fury is one of the few humans they actually trust so they stick around him when not on missions or off doing their own thing.
Also because of Fury, Absols around the world began to be recruited by governments in order to prevent potential disasters from occuring!
And that's about it for Fury haha. Next up is another drawing of Bruce and his team, except this time as Bruce, not Hulk.