The delays seem tied to different colors of cover. One customer said that customer care told them the “delivery date for WiFi-only, merlot with Special Offers is in fact June 21. The soonest I could get the black is May 3rd. I am unreasonably disappointed.” Another cause for delay is disabling the Special Offers.
Customers who want their Oasis as soon as possible might do better to order it with Special Offers intact and pay the fee to disable them after it arrives. (The option isn’t available yet, but then the Oasis hasn’t been released yet. I don’t see any reason why they wouldn’t enable buying off the Special Offers the same as they have with every other Kindle or Fire.) Here’s the page with instructions for doing that.