The Angel Voice anthology of stories actually predates the Type Moon company, and the content contained by Nasu and Takeuchi were made, as far as I am aware, indepdently of the other. At the very least I do not believe Takeuchi had Nasu write for him, and Nasu's story is completely imageless.
The anthology was written around "angels" as a theme, but how well you feel Nasu and Takeuchi's contributions fit said theme is up to debate. I'd certainly claim that while Angel-looking characters appear in Notes, they are far from the main focus. As for Takeuchi's contribution, I've never read it as I can't find it anyway.
Angel Voice is not merely here because it contains the earliest known published work by Kinoko Nasu (for all I know it wasn't), but that it contains the first published appearence of the setting that would become known as the "Nasuverse" - with his contribution - Notes.
Notes is set in the far future of a "bad ending" for (humans at least) in the Nasuverse, a post-apocalyptic earth ravaged by the appearence of the "Aristoteles" or "Types", the ulimate beings of various planets, who arrived to wipe out all life. The story focuses on Gun God, the last surviving un-modified human and his encounters with a mysterious Angel in his apartment. The Concepts that originated here like "Types" are still relevant to this day, and the Black Barrel originated here, with his use of it to kill Type Venus being what earned Gun God his name.
Takeuchi's contribution - canaan-vail Clockwick is far less relevant as it has never been referenced since.
It is similarly set in a post-apocalyptic world and deals with the robotic main character - Gabriel - dealing with the fact she'll run out of power and die in 5 days.
Other than that, the works have no connection.
The first three characters who appear on the banner are the cover-girl of Clockwick, Gun God and the "Angel".
A as of yet incomplete novel series Kinoko Nasu began in 2000
A complete short story
A series of light novels.
The now defunct Type-Moon mobile site. While it was right at the forefront of their brand for a while, the fact that it is now down and most out-of-site mentions of it seem to have to have stopped alongside the site itself going down.
The majority of content on it seems lost with the site due to most links on Archive.org leading to just white screens or redirecting to the desktop site. Information can be found on Japanese fan wikis but A: I can't read the language and B: machine translation of said wikis hasn't been much help.
It seems that before the series was dropped it was the closst thing to a "fifth pillar" of the Nasuverse, not only were the protagonists basically the mascots of Type-Moon for a while via their prominent featuring on the modile site but a number of spin-off material like Drama CDs, manga adaptations and they even recieved their own dedicated episode of Carnival Phantasm. It even recieved its own artbook - Mahou Hako Chronicle. It was iconic enough in my eyes that the two main characters - Hibiki and Chikagi appear so prominently to the right of this page.
It seems to have had some sort of story - or at least enough illustrations to suggest one. Based off the Drama CDs, manga, their Carnival Phantasm appearences and the wiki, it was set largely in the Classic Tsukihime world and dealt with the antics of Hibino Hibiki (Orange) and Katsuragi Chikagi (Green) as they work at the Café Ahnenerbe.
Hibiki is your classic "cute airhead/manic pixie dreamgirl" character while Hibiki (as the twintails would suggest) is a tsundere who serves the "straight-man" for the purpose of the jokes. Whether or not the romance between the two characters is something that was actually there or just played for laughs is something I don't really know but the two are definitely supposed to be close. Alongside them are the owner of the Café George, the perveted sentient phone... Mr Cellphone. Not working at Ahnenerbe but attending the same school as Hibiki and Chikagi is Church executer-in-training Sugata Sunao. Based off segments in Carnival Phantasm and the manga Hibichika timethen Hibiki, Chikagi, Mr Cellphone and Sunao seem to be the central cast, as only the first three appear in Carnival Phantasm and the latter has a prominent appearance in HibiChika time.
The Drama CDs and manga, Starlit Marmalade, seem to be an origin story or prequel explaining how Hibiki and Chikagi met at school and have a far more serious tone than Hibichika time. Unlike the low-stakes comedy of that manga, these tend to focus on more classic Nasuverse elements such as magecraft, as well as actually having a character arc for Chikagi at least as she learns to let her guard down and be more personalable - at least around Chikagi - and deal with her inferiroity complex around her sister. It also has some honest-to-God antagonists who actually try and threaten the MCs.
There are 2 volumes of the Drama CDs, the first of which is almost completely focused on Chikagi and her deal with her sister and is completely set at school, the second is closer to the "status quo" of the other series, including the Café and Mr Cellphone as well as dealing deeper with lore around Holy Scriptures. The manga only adapts the first volume of the CDs, so you'll have to listen to the CDs to get the full story.
Thankfully, fan translations of Carnival Phantasm have been out for years, the manga can be found on most "read manga online" websites, and the Drama CDs have been uploaded to youtube and translations exist - although, the translation for volume 1 has added narration for unknown reasons. Link to the fan translations of the CDs can be found here, but just in case it's a step too far, I won't link the videos themselves.
Maho Tsukai No Hako could honestly get its own dedicated page if there was just a little more material out there, but with the "main" content inaccessible to me I will have to settle for this for now - unless it turns out there is a full archive of the site somewhere out there, in which case I might give Mahou Tsukai no Hako its own page.