Here's what I found out about imgur filenames:

For any Imgur image a typical URL and naming scheme would be:
https://i.imgur.com/XXXXXX.jpg = 4288x3216 px : large original with 4:3 aspect ratio.
https://i.imgur.com/XXXXXX‘‘‘h‘‘‘.jpg = 1024x768 px
https://i.imgur.com/XXXXXX‘‘‘g‘‘‘.jpg = 728x546 px
https://i.imgur.com/XXXXXX‘‘‘m‘‘‘.jpg = 320x240 px  : 4archive uses this one as thumb
https://i.imgur.com/XXXXXX‘‘‘b‘‘‘.jpg = 156x160 px
https://i.imgur.com/XXXXXX‘‘‘s‘‘‘.jpg = 90x90 px

Which translates into archive links:
https://web.archive.org/web/0/https://i.imgur.com/XXXXXX.jpg
https://web.archive.org/web/*/https://i.imgur.com/XXXXXX*
https://archive.today/https://i.imgur.com/XXXXXX*
https://desuarchive.org/_/search/filename/XXXXXX*/order/asc/
Specifying exact file extension is not required, Imgur automatically corrects it when needed.

Twitter files also come from single domain:
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX.jpg
But they might come in different sizes depending on what parameters are sent to the server.

https://pbs.twimg.com/media/XXXXXXXXXXXXXXX?format=jpg&name=4096x4096 = 4096x4096px
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX.jpg:large = 2048x2048px saves as .jpeg
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX?format=jpg&name=large = 2048x2048px
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX.jpg = 1200x1200px
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX?format=jpg&name=medium = 1200x1200px
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX?format=jpg&name=900x900 = 900x900px
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX?format=jpg&name=small = 680x680px
https://pbs.twimg.com/media/XXXXXXXXXXXXXXX?format=jpg&name=thumb = 150x150px

Best way to look it on the archives is therefore this:
https://web.archive.org/web/*/https://pbs.twimg.com/media/XXXXXXXXXXXXXXX*
https://archive.today/https://pbs.twimg.com/media/XXXXXXXXXXXXXXX*
https://desuarchive.org/_/search/filename/XXXXXXXXXXXXXXX*/order/asc/

There are also
?format=gif saves static image as .png
?format=png saves any image, even ones which were originally jpeg, in png codec, .png extension
?format=webp saves any image in webp codec, .webp extension