Eirin is often shown in fan works as using the many rabbits at Eientei, especially Reisen, as test subjects for various drugs and medicines. And according to Cage in Lunatic Runagate, she actually does sneakily give medicine to the rabbits.
An infamous template has "Eirin's shady new drug" as one of its options.
Eirin is often placed as doctor or nurse in fan works for obvious reasons.
She is often grouped with Yukari Yakumo and Kanako Yasaka among the fandom, because their names contain the character 八(which is sometimes read as 'ya'), which when misread, means old hag.
Eirin is sometimes parodied standing in a pose similar to G Gundam character Master Asia due to their similar hair styles and color. This could also be a reference due to the fact that Master Asia is refereed to as "Tohofuhai"(東方不敗) "The Undefeated of the East".
Eirin's name can be mistranslated to mean "spoon". A pun on this is shown in "Staggering Spirit, Keine's Staggering Song", when Eirin throws a spoon angrily at the noticed pun, while the japanese kanji for "spoon" appears right next to Eirin and the spoon.