What is the Vologirakari dynamic like in your opinion? Please don’t ever feel like you have to be less insane about them — the level of freak going on here is too entertaining (and enticing).
Lmao glad the freak is enticing at least!
But, regarding their dynamic - the nuances are subject to change depending on the AU, but in my opinion, one of the most important elements of it is the power imbalance. Namely, this is a god in a relationship with two humans. And an elder god of creation on top of that. That's always going to lend itself to interesting power dynamics, and I love playing around with that.
With Giratina, of course, they're always the one who holds the most power between the three. Their willingness to exert that power fluctuates from AU to AU, but as a general rule, they enjoy being a very dominant, almost possessive force in Volo and Akari's lives. Sex is honestly less of a physical act for them than it is a way to emphasize ownership - they get way more pleasure from seeing their humans submit than they do from any individual acts. Sort of a "sex equals worship" dynamic.
That said, they're not completely selfish. They do have shades of being greedy and possessive, but that's more a result of being banished and isolated without any followers for so long. Volo and Akari are basically the only followers they have, and for all that they can get insanely protective over this fact, they also appreciate it enough to be genuinely sweet and adoring to their humans. They will gladly reel themself in for the sake of Volo and/or Akari's comfort. After all, how can they expect their humans to worship so sweetly if they're not being taken care of by their god?
Volo fits pretty naturally into this dynamic, even with his own selfish and possessive streak, because for all of his self-styled arrogance he does delight in the act of worship. And of course he takes pride in being the favorite of a god! If anything his natural selfishness makes him even more of a perfect fit for Giratina, because the two of them are so alike. They're both greedy, willful things with a grudge against Arceus and a predilection for the darkness. So for all that Volo can be insufferable sometimes, Giratina still loves him. They understand where it comes from, after all. And there is a part of them that needs that kinship.
(Also they find his attitude amusing. Especially in bed. Much more rewarding to dominate Volo when they have to work to make him obey.)
Akari, on the other hand, does not initially seem like she'd slot into the polycule, given the whole "chosen hero of Arceus" thing. But I've always loved to write her as someone with a lot of hidden darkness you wouldn't expect. Typically this takes the form of her chafing against her "hero" persona after the way the rest of Jubilife treats her, and her growing resentment over being singled out and taken for granted. Even in modern AUs where she doesn't have the Arceus baggage, she's usually got some drama going on with her mother as well as feelings of estrangement from more "normal" trainers. Basically, she's got some self-image issues where she feels like a freak compared to everyone else.
And where would a freak feel most at home? With other freaks, of course. Akari tends to latch onto Giratina and Volo very quickly, because she ironically feels way more comfortable in their weird, fucked-up god-worship dynamic than she does anywhere else. It helps that both Giratina and Volo recognize Akari's desperate need for kinship and are happy to fulfill it. Giratina in particular tends to be much gentler with Akari than they do with Volo. They love to dote on her and make her feel appreciated in ways no one else ever has. And like... c'mon. How is a girl supposed to resist a doting elder god of antimatter who calls her "beloved" and fulfills all her secret monsterfucker dreams? She'll gladly sub for that (and Giratina will happily dom).
Anyways sorry for the long post, but TL;DR - Giratina loves to exert their power over Volo and Akari and treats their love as worship, but they also genuinely appreciate their humans and work to take very good care of them. Volo loves Giratina because they're so much alike that he can't find that kind of understanding anywhere else. Akari loves Giratina because she's a closet freak and Giratina (and Volo) give her a place where she feels at home. The result is lots of monsterfucking. And it's beautiful.