Lemme think...
Charizard, Infernape and Pignite are probably best buds since they come from overall very similar backgrounds and train with one another.
Torterra and Hawlucha probably help Bulbasaur with maintaining order at the lab seeing as they use to do the same thing where they lived prior to meeting Ash. Noivern might help them too considering he wants to be like his big bro.
Swellow, Staraptor, Unfezant and Talonflame probably have aerial battles and races, but Noctowl doesn't join them since he's pulling pranks on the Pokemon living at the lab with illusions. Part of me would like to believe that Talonflame is a female and that during and between competing that Swellow and Staraptor try to impress Talonflame and Unfezant respectively with aerial antics.
Heracross is out after Bulbasaurs bulb and Torterra's tree sap and terrorizing the sweet smelling grass types.
Bayleef is standing on a hill waiting for Ash. She knows that he'll come eventually. She missed her chance to meet him during the school trip, but he'll definitely come for her during the world championships in his time of need...... right?
Sceptile and Snivy are just chillin' like villains under a tree.
Leavanny is making leaf cloths everyday for everyone at the lab, and makes beautiful cloths for Hawlucha whom loves to make an entrance every single time there's a fight.
Palpitoad has a cult of Poliwags, Poliwhirls, Poliwraths, Politoads, Woopers and Quagsires hidden deep in the swamp at Oaks lab preparing for the day they will ascend above the petty mortals.