In previous posts, I gave a run-down of the Oeridian, Suel, Flan, and Baklunish pantheons individually. They share many (most) deities, but there are interesting omissions and overlaps. The Flannae Gods are ubiquitous; they found their way into the common pantheon of the Flanaess. The Gods of the Bakluni are the opposite; Istus, the Big Goddess of the pantheon, is unique to the Baklunish, and only appears as a prominent figure in those places with a significant Baklunish population. There are some "obvious" groups of deities; the Oeridian Gods of the Winds, for example, or the Divine Pair of Heironeous and Hextor.
Some deities, such as St. Cuthbert of the Cudgel and Pholtus, seem to be robust enough to have full-blown religions centered on them alone; the twins Heironeous and Hextor could almost be said to constitute a dualistic religion. Medegia being the center of Hextor-worship, Almor being the center of Heironeous-worship, and each mortal enemies of the other, influencing the policies of the secular states around them in their religious quest.
We also have the problem of the "Old Religion" as we see in the module The Temple of Hommlet. The druids seem to have their own faith, completely separate from the religion of the clerics, and yet the Gods of each (notably Obad-Hai and Ehlonna of the Forests) have followers of both clerical and druidic bent. Add to that the fact that Gygax, in later years, said that the druids worshiped not conventional deities but the forces of Nature itself.
How to reconcile all this muddle?
First off, it's important to note that such a muddle is very historical (the example of the Roman Empire comes to mind), and the very fact that there is no clear delineation of religions, deities, and priesthoods is actually a strength of the setting; religion in Greyhawk is messy. In a more "rational" campaign setting, where religion was designed in a more systematic fashion (and I have been as guilty of such in my own homebrew campaigns as anyone), we might miss the sort of organic feel that religion in Greyhawk presents us.
Clerics (and Druids), operate in a polytheistic fashion, although some are henotheistic in nature (other Gods exist, but they aren't worshiped). That is, if a cleric dedicated to, say, Fortubo, was in need of help with healing, he or she might well make an offering to Pelor, despite the fact that they weren't dedicated to that particular deity. I note that Pelor is also a member of the Suel pantheon, so it's perhaps a first-order leap.
A cleric of a deity noted for a more henotheistic approach, such as St. Cuthbert or Pholtus, on the other hand, might well rely on his or her patron deity, regardless of the specific need. But just because a cleric of Pholtus might not be willing (for reasons of ideological and theological purity) to make an offering at a shrine of Wee Jas, the reverse is not necessarily the case. An adherent of Wee Jas might well be more than willing to make an offering to Pholtus, because Wee Jas isn't so picky about exclusivity. The cleric of Pholtus who does so, on the other hand, might well find his fifth-level spells being withdrawn...
The question of clerics vs. druids, and the issue of the "Old Faith" is an interesting one. On the one hand, we have references to druidry as "the Old Faith", utterly distinct from the religion of the clerics of St. Cuthbert (and presumably the rest of the Gods and pantheons), and Gygax's statement that Druids worship Nature itself. On the other hand, we have the fact that the Guide to the World of Greyhawk states clearly that several deities can have servants of both the clerical and druidical classes. Maybe the Nature-worshiping Druids are the "old faith", and those who worship conventional deities are regarded as interlopers. The monolithic structure of the druids is already cracked by the module "Dark Druids" by Pied Piper Publishing. Maybe there are more fractures than we have been led to believe...
On the whole, I think the less-than-systematic reality of the religions of Greyhawk, and the relationship between some deities and pantheonic religions, as well as the lack of clarity vis-a-vis clerics and druids, adds a great deal of color and flavor to the World of Greyhawk. Just as in the real world, we see different people with different approaches to particular Gods, and no One True Way.
Let a thousand flowers bloom...