There's some sort of hierarchy in Briar's team and they interact based on that...

Talonflame is considered by the others as the leader of the team, not only because he's Briar's ace but because he has a very responsible and respectable personality! Houndoom is considered the right-hand-man or second-in-command, he's also the brawn or the muscle of the team because, unlike the rest, he was actually trained with Pokémon Battles in mind. Charizard is the third on the list, because despite not being a very great leader or a super intimidating Pokémon, he's one of the oldest members in the team so they respect him for that... He's the brain of the team hehe. These three are part of Briar's original team in Kalos so they're the big three, the "Victory Trio".

The rest of the team (Chandelure, Volcarona and Nickit) are not part of the "Big Three" so they're more like followers. Although Nickit got a reputation of her own because despite being the youngest, her spoiled and princess-like personality lets her get away with everything bad she does lol When she causes mischief and makes someone else angry, she goes to Houndoom and gives him puppy eyes so he protects her from any Pokémon LOL

For jasmine:
Roble(Trevenant): Jasmine's ace and first pokemon Behaves like the big brother and mediator of the party.

Algodon (Whimsicott): the little guy of the team has no concept of personal space so he is always Climbing on Roble's or Andes's back

Seta (Breloom): Really attached to Jasmine and likes to act as her personal bodyguard she tends to spar a lot with Roble and holds him in high regard, She also finds Demeter Obnoxious

Pino (Abomasow): Big hearty guy of the team, if the team would be a family he probably be the dad, tends to dote on Algodon and seta

Andes (Torterra): Lazy and tends to sleep most of the day both Seta and Roble think that he should train more so they tends to lecture him about responibility often.

Demeter (Sawsbuck): Thinks that she is better and more regal than the rest of the team, except for Roble who she is scared of, most of the team don't take her that serious tho except for seta who sees her as her rival.

Given all they'd been through together, Odd's team is decently close knit, but they all have their own quirks with each other:

Mauve, despite still holding onto some of her snark in a lot of their interactions, is friendly with most everyone on the team, wanting to be a source of reliance and comfort as Odd's defacto ace. She's closest with both Yggy (him being a shoulder she leans on whenever she's struggling with something she doesn't want to tell Odd) and Kat (the two probably being the most openly friendly/comfortable around each other, as well Mauve being the most willing to open up/level about something on her mind with the Houndoom)

Yggy serves a very supportive role in the team's family dynamic, serving as the strong silent type that the other mons turn to for wisdom (which can take the form of gentle nudges or firm putting-a-foot-down depending on how patient the Torterra is feeling). Closest with Kat, the two serving as the "Veterans" of the group, being under Jeri's trainership before Odd.

Kat gives off sort of a big sister vibe for most the other mons of Odd's: both in a "chill, friendly overseer" way and a "occasionally liking to bully the others for a laugh" way. Closest with Yggy and Mauve, the later being the mon she can most openly riff with, which the Houndoom is thankful for.

Barb is, by default, very friendly and chipper, the Crobat being something of team mascot material and always wanting to chatter with the rest of the team, most of them being thankful for the brightness she provides (though a little less so for Mauve who, while still liking her deep down, can get a bit annoyed by the bat). Closest with HAL and Joseph, the three being of a "B-Team"

HAL, while not overtly standoffish and still liking to spend time with the group on occasion, is the most aloof on the team, the Magnezone liking to go off by themselves to get into personal projects. Despite this, they share an odd bond with Barb, them at times liking to have Barb as a parallel play member whenever HAL's getting into an experiment.

Joseph is something of a baby sibling of the group, the Dracovish similar to Barb in a way by wanting to be openly friendly, though being a bit undercut by their shyness. Closest with Barb and Mauve, the latter the Dracovish views as something of a mentor figure.

Tyler's Pokemon interact with each other quite a lot!
-Dragonite is usually the big sister that watches over everyone, especially towards Cloud the Eevee, as she sees him as her baby brother. Though she does have to break up fights from the others
-Cloud is the little goofball that gets along with everyone on the team, he'll normally try to copy whatever they're doing or ask to play
-Scyther is more stoic, but he helps around with looking after the others, he likes to help train Cloud. He argued with Charizard a lot though
-Oricorio is the cheerful gal who always lights up the room, like Cloud, she's always cheers people up. She also loves dancing with Togekiss and Cloud
-Charizard is pretty much the Shiny Wooloo of the group, always grumpy and practicing on his own. He gets easily frustrated and would argue with those who try to calm him down, especially Scyther and Dragonite, who's as hotheaded as him. Though he has a soft spot for them
-Togekiss is a tad airheaded, usually doing his own thing and acts as almost like a polite Butler to the group, as he helps feed them when it's dinner time. He's surprisingly the smartest one of the group and would share Oogway levels of wisdom. He also loves contests, so he loves to dance with Oricorio and Cloud