Well I can try. Just bear in mind that most of this is hearsay. I HAVE grown a lot of these (or have seed and am planning to) but only in experimental amounts which wind up in vases; I just don't have the ACERAGE to grow them in the quantities one would need for consumption.
The oldest kinds of wheat are einkorn (Tricicum monooccum)and Emmer (T. diooccum). Both have grains that do not thresh free easily and heads that shatter readily so cleaning the grain is a PIA. Einkorn is generally only still grown and eaten in some pretty obscure areas It's grains tend to be small as well as hard to thresh.
Emmer is what the ancient Greeks and Romans ate. It's basically einkorn tetraploided which happens naturally from time to time (in fact when I grew my einkorn, a few plants did it and wound up looking far more like emmer than the rest of the einkorn.) Emmer isn't as popular as it once was, but you should be able to find it at most health food stores (under it's Italian name of Farro)
At some point emmer crossed with a kind of goat grass and then doubled again, making spelt which is technically hexaploid 9f you are counting each copy as a copy, regardless of what species it came from). this later crossed back to another wheat found most of the modern wheats which are octo
Which ones you can eat depends on what kind of gluten you have a problem with. A lot of people have their problem with the gluten of the one for bread wheat. Some have a problem with the goat grass one, which knocks out not only bread wheat, but spelt durum, poulard (a kind of giant wheat, in both grain and plant) and rivet (T. tugitum) My Grandma was like that, she was actually wheat allergic, not gluten allergic.
I think that Emmer and Einkorn are a little bit easier on some people, since they don't have the goat grass gluten.
There are also a handful of really obscure species that have totally different crosses. There is a second wild species called Uratu which, when doubled forms something called Timopheevi wheat which is only found in some parts of Middle asia. Others in that group of weirdoes include Vavilov wheat, Isphanii wheat, Pterosky wheat and so on. These all however are pretty hard to get (there's a guy in Canada who has all of them (Prairie Garden seeds I think) but you have to be willing to take the risk of it not getting through customs.)
Outside of those I get a bit faded. I know that for those people who have a problem with barley gluten, the kernels of Job's tear are often a good substitute. Though in that case, your problem will be finding seed for the eating kind (the kind you string on necklaces is just as edible inside, but you'll need a pair of pliers to crack each seed open and get the hull off. I think there is one person in the SSE who is offering an eating one, but if I'm wrong (or he doesn't have it anymore) you'd basically have to do what I do; visit a Chinatown herb shop every week and hunt for the few kernels the hulling and polishing machines missed (and the machines are getting better at not missing any.)
Whoopsies! 
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