Who would have succeeded Edward VIII?

A queen-regnant’s husband can also be a king-consort; as was Phillip II of Spain (in relation to England), Henry Stuart, Lord Darnley, David Soslan, or Francis of Assisi of Bourbon. But William of Orange insisted on becoming sovereign alside his wife. He didn’t want to be a mere consort and wanted to reign ever if his wife died. Parliament agreed after Mary declined to reign alone.

I assume they’re still officially nobility, since they are after all in the line of succession. But they really don’t have titles at all, not even The Earl of Throatwarbler and Lady Mangrove or some such?

No, they are neither royalty nor nobility. After all, the royal family has to end somewhere, since otherwise eventually everyone gets to be royalty. They are commoners, and would only become royalty if their uncles and all their uncles’ descendants died.

One older brother, and one older sister. And like you said, they were from her mother’s first marriage to a minor German prince, so they didn’t count.

You left out lots in between the last of the Kents (Princess Alexandra and her descendants) and the Norwegian royal family. There are all of the Lascelles (descendants of Mary, Princess Royal, only daughter of George V). There are also the Duke of Fife and his family (descendants of Louise, Princess Royal, eldest daughter of Edward VII).

I’m not familiar with the Australian constitution, but the Statute of Westminster’s preamble stipulates that any modification to the succession to the throne requires the approval of every Commonwealth realm. So if the UK wanted to allow gender-blind succession (or allow Catholics to become the monarch), every country that has Elizabeth II as monarch would have to agree. And I wouldn’t be surprised if it required to amend the constitution of all these realms; some of them, such as Canada’s constitution, are very hard to change. This said, I don’t think this disposition has ever been tested in court, and being part of the preamble and not of the Statute itself, it might not be enforceable. We’ll only know for sure when and if someone tries to modify the line of succession.

Regardless of the Statute of Westminster, in the Preamble to the Australian Constitution there is:

However, presumably the UK Parliament, in the Statute of Westminster, did limit its power to change the succession by requiring the approval of other countries in the Commonwealth.

To prevent this situation occuring with Princess Margaret’s children her husband Tony Armstrong-Jones was created Earl of Snowden. By the time Princess Anne got married it wasn’t thought to matter so much (or none of them liked Mark ‘Foggy’ Phillips enough to do it)

Or rather Mark Phillips refused the peerage that was offered to him.

And Princess Anne declined her mother’s offer to create Peter a royal prince by letters-patent.