Boy, this is a cool thread.
Well, real-world mythology has had a certain degree of impact on my homebrew campaign deities, but more or less due to conscious choice. I was more or less trying to go for something which fit my campaign world, as well as drew upon familiar threads.
For example, the key idea behind my campaign pantheon is that there are no variant names for the gods, ala Kalamar; this is because the gods are a present force in the world. They grant spells to their clerics, they sent their servants to the mortal plane in certain times, etc. Thus, since the deities do "exist," there is little, if any, room for variance. Thus, unlike many real-world religions, there are very few off-shoots of a religion. If a faith truly strains from the spirit or intent of a deity's dogma, then their priests know it---loss of spellcasting ability, punishments, etc. IN this way, it's not like the real world. Several real-world cultures had the idea of a Sky-Father/Ruling God idea (Zeus, Odin/Thor, Indra, Dadga/Taranis, etc.), & these deities had similar traits, but they were those cultures interpretations of that deity; whereas IMC, the god states "I am the Sky-God!" & there are no differences between cultures about the god's attributes.
When I designed my pantheon, I did a fair amount of research on various real-world mythologies, & tried to look at the similaries. Then, I wound up amalgamating them to 1 degree or another, & I had a deity for my pantheon. For example, my War God is a sort of mix of Ares, Heimdall, Tyr, Nuada, & various other war gods: he lost his right hand (Tyr) but had it replaced with a silver prosthetis (Nuada); his weapon is a magical sword (Nuada; maybe Heimdall), blood red in color (War from the Piers' Anthony books); he also carries a horn (Heimdall).
However, an interesting side-effect of all this is that most of my campaigns deities are actually True Neutral in AL: mainly because they represent several positive & negative aspects of their portfolios: the War God is a god of conflict, whether wild, chaotic battle, orderly tactics, aggresive conquest or active protection. He also is a god of competition---a role he assumes frequently in times of peace. Other examples include the Sky-Father deity who destroys & brings life (the thunderbolt & the fertilizing rains), the Sun/Fire-Goddess who also does the same (bring needed heat & light which can nourish or destroy), the Sea/Water-God who both floods & fertilizes, & the Mother-Earth/Land Goddess who destroys with volcanoes & earthquakes yet provides fertile soil & minerals.
But, I also decided that theism wasn't the only viable religion IMC; I essentially had each divine spellcaster class, as well as monks, serve as the priest for a different religious belief system. Clerics, as well as paladins, serve the gods; Shamans are animists; Druids, as well as rangers worship nature as a sentient force (though not as a deity); Shugenja worship the Great Kami (a sort of deity worship that interprets the 4 most powerful elemental gods as superior spirits); Adepts worship demi-deities, celestials, fiends, local spirits, & the like; Monks, as well as sohei, follow an agnostic religion focused around self-discipline & self-improvement (sort of like Buddhism, IIRC)---out of all of them, they have the most diversity since there phiosophical tenets can vary, unlike the dogma of the deities.
Along the same lines, the king IMC's main nation is somewhat Arthurian---has a magic sword, is a renowned hero, believes in the cause of good, etc. There is a powerful wizard ally to the king, ala Merlin. The king's champion is a warrior of great renown, much like Lancelot (though who lacks that knight's desire for his queen). It's all there, to a degree, though I was aware of it from the get-go.
So real-world mythologies/religions have deifinitely had an impact on my campaign, but I definitely planned that from the get-go.