Once you have settled on your character guidelines (discussed here) then you need to think about adventures. For myself, one of the big attractions of running a Greyhawk campaign in 4E would be to run a new generation of players through some of the classic early adventures. GH does have a lot of background and history so there's no reason you couldn't just create your own, but you probably don't need a ton of help with that.
As far as creating your own 4E adventures with a Greyahwk flavor, I would say the two main elements to keep in mind are organizations and monsters. There are a lot of organizd groups in Greyhawk from orders of knighthood to political groups to religious groups. The Big Three of Evil in a classic campaign are Iuz, the Great Kingdom, and the Scarlet Broherhood. Other factions and areas of interest include the Horned Society, the Bandit Kingdoms, the Drow, temples to Nerull, Ralishaz, Incabulos, Hextor, and the rest of the major evil gods. Much of the opposition in Greyhawk centers around humanoid races like orcs and hobgoblins and norkers (don't forget the norkers!) but the religious and political conflicts alo mean that other human factions make good opponents as well whether it's Nyrond vs. Aerdy, Keoland and Veluna against the Baklunish coming in from the west, or more localized unpleasantness around the Theocracy of the Pale and its neighbors. The mysteries of Blackmoor and the Land of Black Ice have possibilities (especially for Paragon and Epic levels) as does the far south with Hepmonaland and the Amedio Jungle. Maybe the depths of the Nyr Dyv hold secrets yet unlocked. Vecna and Kas might also serve as high level threats, and there is always the legacy of Acererak.
When it comes to published adventures we are buried under choices. Let's talk about some of them:
Heroic Tier: Well the Temple of Elemental Evil is the obvious choice and it's enough to run your players through the entire range of 1-10. At least I think it is, and I'm testing that theory right now in one of my campaigns.
If you don't want to commit to that there is also the Saltmarsh series, specifically set in a coastal region of Greyhawk. They are a pretty nice mix of exploration, problem solving, and combat, though much of the fighting is towards the end which might not make some players happy. I'm pretty sure there's enough there to work PC's up to level 2 if you use some skill challenges during the haunted house part of the adventure and even in town for the more social players in the group. From there you have the followup Danger at Dunwater which also has a nice mix of combat and roleplay and could use some skill challenges as well. It also has some underwater action which can make it feel truly exotic, especially at a low level. The final part of the trilogy is The Final Enemy which is almost totally underwater and is mostly combat as the PC's invade a sahaugin lair. I can see some level issues here but they should be manageable. I'm thinking this series could be arranged to where the party is level 5 or 6 by the time they finish it up.
Another personal favorite is Against the Cult of the Reptile God which was a really good little adventure until the end where an NPC was needed to weaken the final bad guy so that a party of low level characters could take it on. With the more mechanically controlled levels in 4E I think it would be pretty easy to find a mid to high heroic solo creature and not need the NPC assist. If nothing else, it's a good way to work in a young dragon to an early adventure.
There are always the B series adventures too - B1 is OK and has a few memorable rooms but really only exists to give some structure (and a map) to do whatever you want to do. B2 is the old classic so many of us started out with and is not difficult to adapt to 4E's encounter system. Treat each lair as a 5 encounter mini-adventure, rework the ogre and the minotaur as solos with a level adjustment, and you should have a nice little starting area. B3 was never my favorite but the frozen palace could certainly be worked up as a 4E site. B4 could be used as the start of a whole lot of desert adventure by placing the Pharoah series nearby. The Sea of Dust seems like the most likely place for this kind of thing and you would need to come up with a rationale as to why a low level party is running around an area like that but it does have potential.
For the middle levels the Slavers series could be a core to build around. The first one is a tricky thing to convert as it's a very linear tournament adventure with some unique and way overpowered opponents. A2 is pretty straightforward as is A3 and then A4 could get a little weird again as it assumes the PC's are captured, which they ALWAYS hate. I might have to look these over again and I would carefully consider how you want things to end up with the Slavers and let that guide your planning.
Other good mid level adventures include White Plume Mountain, Lost Caverns of Tsojcanth, Forgotten Temple of Tharizdun, Ghost Tower of Inverness, Tamoachan, and maybe even some of the X modules like Isle of Dread. They tend to involve exotic locations, some interesting opponents and traps, and best of all they tend to be short enough that your players won't get tired of them before they finish, unlike some super-modules.
For Paragon the obvious choice is to go Against the Giants, then into the Depths of the Earth and against the Kuo-Toa and the Drow. That's really enough to keep a group busy for 10 levels I would think. If this is your plan for Paragon then I would make sure my group got to do some traveling during Heroic so that they get to see some of the Flanaess besides it's basement. Other Paragon choices include the Tomb of Horrors and the Barrier Peaks, both of which could probably be worked in during the other ongoing missions against the giants and the rest. I considered at one point taking Dwellers of the Forbidden City and making it into a Paragon adventure - I think it has a ton of potential for that. It makes for a nice campaign shift too if you play through heroic in a civilized area - the party makes a name for itself and then gets asked to help or lead an expedition down to the ruined city in the jungle - sounds good to me!
For Epic it might be time to take down a big nasty dragon that's been interfering with their travels and the nation, say the Yeomanry or Keoland. An old Suel Arch-Lich might be waking up out in the Sea of Dust and need a lesson in good behavior. The Circle of Eight might need some help recovering an artifact, leading into the Isle of the Ape.It could be time to take down the Scarlet Brotherhood once and for all and then perhaps it's time to take the fight to Iuz himself. Spending the first half of Epic tier fighting a war against Iuz and his demonic minions would be a pretty satisfying experience I think. Eventually it could come down to a direct confrontation and a chance to custom build a say, level 28 solo. Then of course Lolth is still waiting in the Demonweb Pits and sooner or later it's time to finish the job they started back at 11th level and stop the Drow demon-goddess for good.
As far as ridiculously high level characters running around Greyhawk, well, look at some of the original player characters and their unique abilities - clearly EGG was pretty flexible in those early games and looking at the 1E Rogues' Gallery and some of the characters written up in Dragon and the EX adventures you get quasi-deities and hero-deities like Murlynd (who uses dual six-shooters) and Kelanin not to mention that ascension to demigodhood is expressly spelled out in the Deities and Demigods book! So don't be afraid to have a few level 25's taking a hand in things in the form of your party. Deities come and go, nations rise and fall, and races ascend in power then get banished to the underworld - go ahead and let your players make a difference! It makes the campaign that much more memorable and gives the next Greyhawk campaign a fresh starting point.
Some ideas on conversion, based on doing a few:
Reference the actual original modules, not your memories of them. Things get fuzzy over time. If you're going for the original experience, stick with the module. If you're going for what you remember, then go with that - it might be more fun! But at least take a look at what was actualy in there.
Don't get caught up in the levels or hit dice - mechanics change. Flavor is more important than numbers - it is Against the Giants, not Against the Ogres. Descriptive text is edition-neutral! Illustrations are edition-neutral! Even maps are edition-neutral, though you may want to put a little more detail into some of them rather than sticking with so many bare stone rooms.
Don't worry about the original treasure - use the 4E treasure system. Descriptions of art objects, jewelry and gems are still valid even if the value changes. Try to find similar magic items to the originals, but stay flexible. Lose the cursed stuff unless it makes for a particularly interestng encounter and even then use them sparingly.
Keep the traps. That's part of the old school flavor and there are lots of example conversions in the DMG 1 & 2. Plus 4E characters are pretty tough and they aren't going to be killed by a 10' deep pit at 1st level.
Encourage thinking and be specific in play - don't fall prey to "I search the room...22 Perception. What do I find?" Most old modules have things in specific locations like under a loose stone in the floor, behind the bed, in a locked drawer in the desk. Ask each player what part of or thing in the room they are searching - this makes it a little more interesting and ensures that the character with the highest perception doesn't automatically find everything. Limit it to one thing or area per round of searching so everyone gets a fair shot.
Look for places to add in some skill challenges - they break up the combats that comprise most of these early adventures and give different characters chances to shine. Deciphering inscriptions, opening a special secret door, climbing across a dnagerous area (like the disks over the boiling mud in S2), answering a Sphinx's riddle or other challenge, or talking one's way past the otherwise neutral guards all make good skill challenges and can be surprisingly fun.
Anyway that's my outline and guideline for running classic Greyhawk in 4E. The mechanical changes do have an impact, but the world is the same. If you're uncovering agents of the Scarlet Brotherhood in Keoland, negotiating with the Elves of Celene and Highfolk to help drive the hill giants back into the Yatils, Fighting Yuan-Ti in the Forbidden City, ambushing one of Iuz's patrols in the Shield Lands, or taking over the throne of one of the Bandit Kingdoms, then it's still Greyhawk, and it's still a blast.