Nagae (永江) means "eternal river", and Iku means 衣 = "clothing" , 玖 = number "9" or "black-colored jade". So together, her name might means "a black jade in (scarlet) clothing at the eternal river".
Iku's spellcard declaration pose and some alternate special move poses closely resemble John Travolta's dancing pose from the disco movie Saturday Night Fever, which many doujin work make fun of by linking her to disco dancing. To a lesser extent, they also resemble Bass's lightning attack pose from the game Mega Man & Bass(which has led to shipping Iku and Bass together), as well as the start-up of super robot Great Mazinger's move, Thunder Break. Fanworks also revolve around parodying Micheal Jackson.
"Iku" can also be spelled as an intransitive Japanese verb （行く） that literally means "going", but its phonetic version （いく or イク） is better known as a phrase uttered at... "key moments" in h-anime. Raunchy jokes commenced almost immediately.
Iku's dress resembles that of a Spanish Flamenco dancer, and her movements and poses look a bit like dancing. However, her profile states that it's a special dress, granting the owner the ability to fly. Maybe it's a reference to some dances, where it looks like the dancer is flying.
Her profile suggests that she is a Youkai of oarfishes. In Japanese, oarfishes are called "Ryūgū-no-tsukai" (リュウグウノツカイ or 竜宮の使い in Kanji), which literally means "messenger from the Dragon's Palace". In this case, a dragon is considered as a god of water. Her shawls (and probably the long ribbons on her hat) are apparently modeled after the shape of oarfishes, which have thin, elongated bodies and red fins.
Some of her spell cards in Hisoutensoku revolve around the names of fish, and involve her shooting a drill out of her hand(as well as a bigger one). This could be a reference to the infamous Giga Drill Breaker attack from Tengen Toppa Gurren Lagann.
The phrase 「ｷｬｰｲｸｻｰﾝ」 or "Kya—Iku-sa—n" (in half-length katakana) has become a meme relating to Iku, which originated from another meme, 「ｷｬｰﾘｭｰｻｰﾝ」 or "Kya-Ryu-sa-n" (note: Ryuu means "dragon") in response to dragoons in Final Fantasy XI.