First they started as promo videos in a website to promote the anime series: "Melancholy of Haruhi Suzumiya" to an english public but I heard they are available on some physical release.
Known lost extras:
ASOS Special Announcement
ASOS Web Only Episode C
Existence Unconfirmed:
The Adventures Of The ASOS Brigade™ - Episode 006
The Adventures Of The ASOS Brigade™ - Episode 007
The Adventures Of The ASOS Brigade™ - Episode 008
The Adventures Of The ASOS Brigade™ - Episode 009.1
Found extras:
The Adventures Of The ASOS Brigade™ - Episode 00
The Adventures Of The ASOS Brigade™ - Episode 001
The Adventures Of The ASOS Brigade™ - Episode 002
The Adventures Of The ASOS Brigade™ - Episode 005
The Adventures Of The ASOS Brigade™ - Episode 003
The Adventures Of The ASOS Brigade™ - Episode 0013
The Adventures Of The ASOS Brigade™ - Episode 009.0
Special Report - US Launch Event
The Adventures Of The ASOS Brigade™ - Episode 004.1
The Adventures Of The ASOS Brigade™ - Episode 004.2
The Adventures Of The ASOS Brigade™ - Episode 0010
The Adventures Of The ASOS Brigade™ - Episode 0011
The Adventures Of The ASOS Brigade™ - Episode 0012
Notes:
Episodes 003, 005 and 009.0 were only partially found but have since been found.
There may be an Episode 009.1, as it is mentioned in the end credits of episode 009.0, however the next episode is a Special unnumbered episode which states Episode 009.1 will not be shown.
The numering of the episodes is inconsistent, but if it isnt a production error, for example Episode 009 goes after 0013 as seen in the Episode 0013 end credits.
There may be Episodes 006, 007 and 008, however these were not included in the DVD release, nor were they posted to the ASOS Brigade website.
There was a second season consisting of Episodes 0.888, 1, 3, 4 and 5. Episode 2’s existence is unconfirmed. Episodes 0.888 to 4 were included on the first US releases of the second season of Haruhi Suzumiya DVDs. Episode 5 is also known as Episode A and was included on the initial US release of the Haruhi Suzumiya Movie.
The second season also has 3 associated special episodes, all of which have been found and are on the initial printing of the US Haruhi Chan DVDs.
Link to all found extras as of 03/09/2021