Mosty things are edible, some just take more creative cooking than others. This includes badgers apparently although I haven't tried them. Old hens were a common ingredient when I was young and even into the 1970s I could buy them from a local egg farm for next to nothing. Skin them, don't bother plucking as you aren't going to roast these old boilers. Draw them, and yes they do reek something wicked. Pressure cooking is good, or a long long slow cook in a casserole, with lots of water and veg/seasoning herbs. At the end you will have a little breast meat that is tender and a lot of fantastic stock to turn into soup.
Unless you have unlimited room you will have to neck your old birds sooner or later, so why waste their carcases?