I have the Living Greyhawk Gazetter. Is that a good source, or I should get that Boxed Set everyone talks about?
I find it much more useful as a DMing or player reference than the earlier 1e/2e stuff. Information is plentiful and easy to find for most things, especially geogrpahy, cultures, and history. Yep it's dry, but you're not reading it cover to cover most of the time. When you really need to know about Urnst or a specific mountain chain or forest etc., this is the best reference IMO.
The 1e stuff, 1983 boxed set, etc. is fine for an overview of the world, and the formatting etc. are flavorful and fun. The writing feels very early-RPG and lacks the easy-to-weave-in approach that makes modern RPG products sing though (IMO). It makes good inspirational material and is helpful to at least skim if you want to understand why so many folks love Greyhawk.
As for the events of the Greyhawk Wars and after included in later publications, they are canon for the large amount of excellent material published during 3/3.5 edition. This includes the detailed and generally very well-written adventures in Dungeon Magazine, the Living Greyhawk Journal background articles, etc. Most of that was written by Paizo under the editorial and authorial tenure of the best Greyhawk loremasters out there (Erik Mona).
If you want to use that material, the Living Greyhawk Gazeteer is very helpful, allowing you to put it all in perspective.
In my opinion the 3.5 material, and the excellent Carl Sargent writing in From the Ashes etc. was Greyhawk's high point, and the plot developments are not very hard to follow.
Read it for yourself, starting with the Living Greyhawk Journal articles if you want light, or From the Ashes if you want really great writing.