Quick Notes on the Less Common Atronachs
I didn't have enough for each of these to warrant them all getting their own posts, so they get a bonus footnote-style post instead.
In-Game Lore
Air Atronachs possess the combined power of Flame, Frost, and Storm Atronachs. They were created by the Serpent (who stole the Mage's Atronach army) and quickly adopted as servants by Mehrunes Dagon.
Fire Daedra are more mundane but dangerous Daedra. They're slightly intelligent and possess some spellcasting abilities. They can only be harmed by mithril or better weapons and greatly resist fire-based spells. Frost Daedra are the same but resist cold-based spells instead.
Iron Atronachs (also known as Earth Atronachs) are composed of both solid and molten iron in a roughly humanoid form. They're from an unnamed volcanic realm of Oblivion, have a relentless appetite for destruction, and are often found in Mehrunes Dagon's Deadlands. Mortal conjurers don't mess around with Iron Atronachs due to a long history of Iron Atronachs going rogue to just destroy everything. Electricity-based spells heal them. Their names often appear with the Daedric clan name "Mynar".
Not much is known about Shadow Atronachs other than that they can be summoned by a conjurer.
Stone Atronachs are made entirely of stone, with four legs, a central body, and one eye. They can be summoned from a variety of sources, including crumbling ruins.
Pop Culture Witchcraft
Deactivated user @mothmaam has an Atronach conjuration spell that, while also summoning Flame, Frost, and Storm, can be used to summon an Air Atronach familiar. You could adapt the spell to account for other Atronach types, and I still hold that you could also shape thoughtforms or servitors to look and work like these Atronachs do.
They are experts in their fields, so you could consider it proper to call on them for different types of assistance:
Air: air- or wind-based spells, anything you would call upon a Flame, Frost, or Storm Atronach for, working with Mehrunes Dagon
Fire Daedra: fire- and heat-based spells
Frost Daedra: cold-, frost-, and ice-based spells
Iron: destruction, heavy duty curses, working with Mehrunes Dagon
Shadow: keeping something hidden, mystery, shadow work
Stone: crystal magic, earth- and stone-based spells, stability
Sources
https://en.uesp.net/wiki/Lore:Elemental_Daedra
https://en.uesp.net/wiki/Lore:Bestiary_A#Air_Atronach
https://en.uesp.net/wiki/Lore:Bestiary_F#Fire_Daedra
https://en.uesp.net/wiki/Lore:Bestiary_F#Frost_Daedra
https://en.uesp.net/wiki/Lore:Iron_Atronach
https://en.uesp.net/wiki/Lore:Bestiary_S#Shadow_Atronach
https://en.uesp.net/wiki/Lore:Bestiary_S#Stone_Atronach
https://the-college-of-whispers.tumblr.com/post/661947710698668032/conjuring-an-atronach