There is some information in their respective books, but it's not much, I'm afraid.

Tasha

Introduction in Tasha's Cauldron to Everything:

Tasha's Cauldron of Everything offers a host of new options for DUNGEONS & DRAGONS, and our journey through those options is accompanied by the notes of the wizard Tasha. Creator of the spell Tasha's hideous laughter, Tasha's life is one of the most storied in the D&D multiverse. Raised by Baba Yaga, the Mother of Witches herself, Tasha adventured across the world of Greyhawk and became the friend and sometimes enemy of other famous adventurers, like Mordenkainen. In time, she ruled as the Witch Queen and later changed her name to Iggwilv - a figure of legend who is whispered about, feared, and admired.

There are also notes from Tasha spread among the book, from which we learn that her aliases are Natasha the Dark, Hura of Ket, Baba Yaga's Daughter or witch by excellence, and that she loves insects, for example.

Xanathar

Introduction in Xanathar's Guide To Everything

Beneath the bustling city of Waterdeep, a beholder crime lord keeps tabs on everyone and everything—or so the beholder thinks. Known as Xanathar, this bizarre being believes it can gather information on everything in the DUNGEONS & DRAGONS multiverse. The beholder desires to know it all! But no matter what the beholder learns and what treasures it acquires, its most prized possession in all the multiverse remains its goldfish, Sylgar.

Again, we can learn some things from his notes throughout the book, like he's glad to live underground because there is no weather, or that he's not sure whether he likes music or not.

Mordenkainen

No short introduction here, but we can learn some things from the notes at the beginning of the book:

Mordenkainen is an Oeridian wizard from the world of Greyhawk who travelled the multiverse with his apprentice Bigby to observe conflicts of all sorts.

Volo

Sprinkled throughout the book are observations and musings from two denizens of the Forgotten Realms: the legendary explorer Volothamp Geddarm (Volo to his friends) and the Archmage of Shadowdale himself, Elminster Aumar.

Here again, some notes throughout the book give hints about the personality of Volo.