they look like some sort of plum. we had a tree like that when i was growing up. the fruit looked the same except is was a yellowy orange color. but the plant itself looks the same.
Based upon the leaf and the fruit this link provides a pretty close match to a wild plum. They are edible but will probably be slightly tart compared to cultivated fruit varieties. You won't die eating them!
Your county has an agricultural extension service/agent, they're paid (by your tax dollars) to help you with your agricultural applications, such as identifying your fruit/trees & such. Check the county govt blue pages in the phone book for the number. Just take them a sample of fruit & leaves, they'll be happy to ID it for you & they're trained to such things, it's their job.
They have all sorts of free AG info & often they'll have classes & workshops available for free or for a modest fee to cover materials. They'll help you with your lawn, your garden, your hops, weed control, pesticide use, etc...
You're paying for it, might as well use it eh?
Regards, GF.
They look like plums, we have the same type here in the Czech Republic. They will be sweet when ripe and make nice wine or sauces. Grab em before someone else does!