My Air Data

If you check your my air app and the data isn't ready yet, would that mean the data isn't ready yet for Oscar also and should you not take out the SD card until my air gets its data for the previous night's sleep?

No. The data is on the SD card once you turn off the machine after a couple of minutes.
MyAir website data has nothing to do with the SD card storage.
MyAir website lack of data just means that when the machine transmitting the data hasn't been uploaded (for whatever reason and it's usually a problem on the website and sometimes that can take days to resolve) and the SD card can be used anyway/anytime for OSCAR.

Example....I don't have any data transmitted to MyAir at all and I still can use OSCAR at anytime I want to.
The SD card is just for data storage to be used by software like OSCAR or ResScan (ResMed's proprietory software)

Wait a few minutes after you've finished using the machine in the morning to let it complete writing to the SDHC Card and confirm that the blue LED Activity Indicator is not flashing before your remove it.

The detailed data written to the SDHC Card is completely independent of the upload to the Resmed Cloud. Resmed devices upload use an internal cellular modem. If your Airsense isn't in Airplane Mode and has cell signal, but you aren't seeing your stats in myAir™, tell Resmed. If enough people complain, maybe they'll do something about it! myairsupport@resmed.com