Mimihagi represented stagnation
Pernida tepeesented progression
Gerard represents Tenacity
And Gerard does not necessarily look like the ACTUAL Thor of lore, unless you're talking about Marvel's thor then yes.
The soul king himself seems to just be a catalyst, in order to keep him in check I would assume the shinigami split him into a certain amounts of pieces. So that way an unemotional being is kept to keep soul society in place. Without his immediate right hand the soul king cannot have stabilized power, without the left hand the soul king cannot progress in power, without the heart, the soul king cannot feel any tenacity or determination to do anything at all but do his own job at maintaining balance. There are most likely more parts to the soul king but the soul king is a Yin/Yang kind of being. You can tell as pernida is a quincy and is white representing yang while mimihagi is black most likely representing the shinigami and is Yin. The heart, Gerard seems to be leaning more tp the actual Yang portion than the yinnportion as the geart itself is typically malleable so the soul king's heart appears no different. In other words, the soul king appears to be the true origin of quincy and shinigami alike, but it's said shinigami made the spirit king so there's some oddity there. Either way all these pieces of thevsoul king under yhwach are the quincy or yang portions of the actual soul king, and we saw one yin portion and that's mimihagi