の and で are particles. It doesn't make too much sense have both right next to each other, but think of it as "(一斉の)で" i.e. "on 'issei no'".
えい!is the Japanese way to shout when trying to put their back into something. You'll hear it in Karate often.
Literally it means, "When I say 'together;' here we go!"
It's kinda funny, because it's like saying "on three," but not actually counting to three because "on three," itself is the count.