I've tried searching
egl, but without any results other than passing mentions of the term. Looking it up on the English version of Wikipedia gives me a song, a rocket launcher, and a cycling team. Searching the Japanese version of Wikipedia mentions two songs (one Russian; one Japanese), that the term is used for headbands, a film, a weapon, a unit, a cycling team, and an asteroid. My Google attempts have been less useful.I'm presuming that the use of the term for headbands is related to the fact that "Katyusha" is a tender diminutive of Ekaterina. It looks like there was a popular Taisho-era song called Katyusha; I used a translator to get some idea of what the Japanese page said, but if that page explained why katyusha is used to mean headband, I didn't see it.
For some reason this was a term I've never really questioned before, but reading it on the Angelic Pretty shopping site today made me pause. Now I'm really curious! Does anyone have a theory?
UPDATE:
thevisual_beast was kind enough to provide a translation of a Japanese Wikipedia explanation in this comment. 