From the Ashes by Carl Sargent on How Do Powers Look Upon Mortals:
"The Powers of Oerth rarely intercede directly in the affairs of Oerth. They expect their servants to be their right (and left) hands in the world...The Powers have an implicit understanding that if one of them should act too directly, others will act in concert to oppose the meddler, for if all acted in such a manner, Oerth would be destroyed by the Powers.
This helps us understand why the demigod Iuz has been able to effect so much evil in the Flanaess. The Prime Material Plane is his home plane, and therefore, he has a direct involvement in its affairs that other Powers do not...One partial exception is St. Cuthbert of the Cudgel. Other Powers allow St. Cuthbert to act in limited ways to oppose Iuz."
Indeed, this Cuthbert-Iuz rivalry is suggested previously in Temple of Elemental by Gary Gygax and Frank Mentzer but it is not explicitly stated the gods overall are barred from Oerth:
"Because of the plots of Iuz and various demons and evil elemental types, St. Cuthbert has become actively aware of events, and has indirect assistance from Beory (who resists elemental destruction). The enmity between Iuz and St. Cuthbert may result in direct confrontation!"
"No god above demigod level may enter the Prime Material Plane of Oerth without the consensus of a majority of the gods of Oerth. A few exceptions to this are Ehlonna, Fharlanghn, Obad-Hai, and Olidammara (who chose the Prime Material Plane as their native realm), Beory (who may actually be the Oerth itself), and St. Cuthbert (who was allowed to come to Oerth to fight Iuz on more than one occasion)."
Older sources paint a slightly different picture than what Carl Sargent initiated in the 2nd Edition era of Greyhawk (if there is an earlier source of this law let know in the comments). Len Lakofka and Gygax seemed to have a more classic mythology flair to the pantheons of Oerth. In addition, Greyhawk Adventures by James Ward states in the first paragraph of the first chapter:
"The gods often visit the Prime Material Plane in avatar form to aid their worshipers or just to enjoy themselves. In one way or another, they influence actions of all creatures on the Plane...For some unknown reason, the city of Greyhawk gets an unusual amount of attention from these deities-at least one of these beings usually has an avatar in the city. Many ballads tell of awe-inspiring confrontations between avatars of opposing alignments on the city's crowded streets."
Syrul lesser goddess of deceit (Dragon #88) "When a member of the Scarlet Brotherhood who is an assassin, illusionist, thief or monk attains the 9th level of experience, Syrul will personally attend the level-advancement ceremony to wish the character "evil-luck". Such a character is granted a vision spell with no strings attached."
To remind you, the Scarlet Brotherhood is comprised entirely of assassins, thieves and monks. Syrul doesn't just visit her special worshippers then, but ALL those high-level characters in the organization. That's not to say the goddess of deceit does this overtly in front of everyone, but she is there in person for a ceremony!
Wee Jas greater goddess of magic and death (Dragon #88) "She can summon groups of lawful undead or lawful dragons (not Tiamat or Bahamut) to do her bidding...Summoned creatures will come to her in Acheron or on the Prime Material Plane..."
Wee Jas is a vain deity, so why wouldn't she want to meddle in mortal affairs? Now admittedly this example is not as concrete as the one for Syrul, but it does infer that Wee Jas can call down heavy aid if she is on Oerth and needs to fight. That's not subtle at all for a greater deity.
Kord, another greater god, is a classic example of meddling in mortal affairs, in the fashion of Zeus, by having actual affairs with mortals! The article in Dragon goes on to explain how a PC can possibly be a child of Kord and the game bonuses inherited. Later sources like From the Ashes completely omit this behavior by the Brawler in deference to the new "non-interference pact".
Phaulkon greater god of air and avians (Dragon #87) "Phaulkon is a relatively active traveler, and enjoys the company of men and elves. He can shape change into any normal or giant bird at will, as well as into the form of an elf or sprite."
Even Kord's dad likes to hang out on Oerth, and though it doesn't state he is promiscuous, there is no reason to believe he couldn't sire hero-gods like his son.
Norebo lesser god of luck and gambling (Dragon #86) "Norebo enjoys visiting taverns and gambling houses in the guise of a cheerful, innocent stranger and setting up dice games against other patrons...it is impossible for someone to know Norebo's true identity unless the deity wills it."
This roguish deity is discreet about his interactions at least!
Heironeous lesser god of chivalry and justice (Dragon #67) "Heironeous often leaves the Seven Heavens in order to move around the Prime Material Plane, aiding heroic causes and championing Lawful Good...he has the power to create an illusion which makes him appear as a young boy, a mercenary soldier, or an old man. In the latter guises he will be garbed appropriately, but he always wears a suit of fine, magical chainmail."
Yes, even the patron of paladins and knights everywhere in the Flanaess cannot help but get involved. He isn't directly appearing in all his glory, but he is there (perhaps even on the front lines helping Shield Lands and Furyondy vs Iuz!) in contradiction to later canon law. Then there is his brother...
Hextor lesser god of war (Dragon #67) "Hextor dwells on the Planes of Acheron but can wander to those of Hell or even Nirvana. Most frequently, though, Hextor treads the Prime Material Plane in search of warfare, aiding lawful evil, opposing good...Hextor appears as a normal, handsome man when in disguise, for he can cause four of his arms to meld with his torso whenever he so desires. His complexion is fair and his hair jet black, as are his eyes. He is well spoken and charming, a hale fellow and a man’s man, yet irresistible to women."
Hextor is MOST FREQUENTLY on Oerth doing his business. Why wouldn't a war god hang out on battlefields with mortals? It's what Ares would do. Speaking of war gods...
Erythnul lesser god of hate and slaughter (Dragon #71) "Erythnul stalks battlefields in order to strike fear and rout whenever possible...when Erythnul engages in combat, his visage mutates from segment to segment, flowing in form from human to gnoll to bugbear to ogre to troll."
Think about this, mean ol' Erythnul could potentially be on the SAME battlefields as Heironeous and Hextor. Erythnul is not as subtle as the brothers though. Oeridian gods don't seem to play by Sargent Law. How about Baklunish gods?
Istus greater goddess of fate (Dragon #69) "Istus does certainly make appearances on other planes, including the Prime Material. Sometimes she is an old crone, other times she appears as a noble dame, then again as a lovely lady or even as a shepherd girl."
Istus is another deity that can meddle in disguise as much as she wants, but she is also responsible for the Oerth-spanning retcon during 1E-2E that was Fate of Istus. I suppose she had permission from a majority of gods for that one...
The grim reaper likes the hands-on approach, do not accept any lesser imitations.
There is more exceptions and instances than I can possibly list in this post. So just saying all Powers are flat-out barred from Oerth is just lazy writing in my opinion (which I never accuse Sargent of being any other time) and it robs the deities of much of their flavor and uniqueness. Was it done for game balance? Most likely. But for years we at least had DM agency to have divine intervention if we wanted as authors heaped us with game stats for D&D gods. No one wants a god-killing Time of Troubles situation like in Forgotten Realms of course. Deities shouldn't be superfluous in appearance like the Syrul example above, nor dropping like flies in the street like Greyhawk Adventures suggests. Also using avatars versus actual deities manifesting on Oerth is a semantic argument. Either they influence mortals directly at will or they only allow exceptions like St. Cuthbert. Whatever you decide for your own game, the examples from Dragon Magazine above are all reasonable ways to reward (or punish) PCs for learning mythic lore and having patron deities by showing the players that the gods are real in the World of Greyhawk.