Here's the calculus of Greg Egan short story collections. Pay close attention!
Axiomatic is... well, axiomatic. It does not overlap with any later collections, and it is essential, since it contains some truly excellent stories.
Luminous = (Our Lady of Chernobyl - "Beyond the Whistle Test") + 6 more stories including the story "Luminous."
Oceanic = (Dark Integers and Other Stories - "Luminous") + (Crystal Nights and Other Stories - "TAP")
So, if you must buy only one Greg Egan short story collection, start with Axiomatic. If you want to get most of his best recent stories, buy Oceanic. Honestly, those two will get you most of his best work. If you want pretty much all of his stories in print, go with Axiomatic, Luminous, Dark Integers and Crystal Nights. If you own Dark Integers and Crystal Nights, Oceanic is completely redundant, unless of course you're collecting the different editions themselves. Our Lady of Chernobyl still contains one story not collected elsewhere -- "Beyond the Whistle Test." If I recall correctly, I have not read this story.
Note that many of Egan's stories are available online from various sources, as documented on Egan's Bibliography page.