Not sure what relation would there be? AEIOU is short for Alles Erdreich ist Österreich untertan in German or Austriae est imperare orbi universo in Latin, or in English "All the world is subject to Austria", as used by Frederick III when he was duke of Styria. But some other interpretations by heraldists were also brought forward. No English was used and I have seen no evidence that would imply Frederick spoke English.

English has around 12-14 vowels, as it varies among dialects. There are also diphthongs and reduced vowels. Your average English speaker would pronounce only one letter in AEIOU as a vowel (E as an [i:]) and other four as diphthongs, while in German and Latin all five letters would be pronounced as vowels.

I'm confused as to what relation are you implying there is.

I am not able to state any sources on this (maybe someone can help out) but it is pretty obvious that the sequence was deliberately chosen. It is the common way to list the vowels in German and thus a familiar line; after all, shorten your motto like this makes only sense if you can make something catchy from it.