Taking a crack at it, though I'm by no means a Lore Master.
Well Ayem Seht and Vehk are Daedric names for Almalexia, Sotha Sil, and Vivec.
Ae seems to be a bridge word, and has nothing in Daedric that would qualify. Draconic language, however, leads to some interesting revelations - if extremely flimsy given the age of the text and the revelation of the dragon tongue in relation to we the players.
What got me looking in that direction (Beyond the fact I am a Dragon Enthuisit) was actually the fact Seht had a "i" at the end of his name. The letter "i" in Draconic is utilized as a personal possessive. And while there is no "Ae" in the Dragon tongue, there is AU...which means "On".
Ayem Au Sehti Au Vehk could thus be translated as Almalexia on my Sotha Sil on Vivec. The possessive nature of Sil is interesting to me, since he is the only member of the Tribunal whom we do not interact with in a meaningful way - having been killed by Almalexia. But given the nature of the Tribunal, that means he was also killed by Vivec...possibly explaining why his is the sole name to have a possessive.
To reinforce my theory that this sermon is speaking about Thu'um in some capacity, look at the line "In you is [...] a seven-syllable spell", Seven Syllables...like a language.
Diving into this further, I started looking for substitutes for Ayem, Seht, and Vehk (A, B, and C).
Ayem is a difficult word to pin down in Draconic, with no words really matching the pronouncing of it. That being said, she is known as "The Lady of Mercy", and surprise of surprises...there is a Draconic Word for Mercy that begins with "A" - Aaz.
Seht actually proved to be the easiest of the three. Turns out in Draconic there exists the word Sil. It means "Soul".
Vehk. Vehk's a hard one. There are no words for "Poet", "Warrior", or even close approximations of Vehk or Vivec. However, he's also the "vi" at the end of ALMSIVI and Draconic does include a word Viir.
Combine it all together and you end up with AAZ AU SILI AU VIIR. A Thu'um of Seven Syllables meaning "Mercy on my soul on dying".
What is death if not the greatest mystery of all?