Now that is a tough question to generalize on. Depending on breed, wether or not it is a sexlink, and the breeding line it came from can all have a drastic impact on how this would be answered.
Having said that many GOOD heritage bred hens can go into their teens. But at that point their eggs per year is likely cut in half. Sexlinks tend to lay better for the first season or two and fade fast from there.
I've got the most experience with your standard breeds. Most of the production drops significantly after the second year. We kept our most recent laying flock of Buff Orpingtons for almost 4 years. That last year (the third year) we were only getting an avg of 0-2 eggs a day from a dzn hens. But, our flock got lots of garden goodies and was free range much of the time as well. And I've been told that can affect their laying rates.
I imagine that you could eat an old hen at any age. It would probably be best cooked for a stew, or a soup, as I imagine they might be a tad tough. My Dad used to get stewing hens back when I was a kid, as they were very inexpensive. He often cooked them in a pressure cooker, to get them tender. He used to do mutton that way as well, to get it tender. Both tasted good from what I can remember.
I have heard that to do a proper "coq' au vin" it was required that you use an older bird. Apparently the flavour is much better, then a younger bird.