I too, have had hens with that squishy swelling between their vent and legs. I have searched and searched for an answer. Hark! I have found it. It is called
CYSTIC DILATATION OF RIGHT OVIDUCT IN LAYER CHICKEN
and here is the link: http://www.tanuvas.tn.nic.in/tnjvas/vol7(5)/218_220.pdf