[Mike Swearingen]

If the stems are so corroded that they just snap off, you can almost bet that the seats that seal against the washers are too.
I would replace all of them with good quarter-turn ball valves.
If you don't care to solder and all of these valves are clearly visible at all times, you can simply use good compression-fitting ball valves that are installed with two wrenches (one tightening, the other as back-up).
You can find them at almost any plumbing supply. Also get some emory cloth or sandpaper to clean up the ends of the copper pipes before installing the compression fitting ball valves. You don't need any teflon tape or pipe compound with compression fittings. The threads don't seal them, the brass ferrule ring does the sealing when compressed onto the pipe by the nuts on the valve.
Good luck!
Mike

 

[Mike Swearingen]

You can use a small screw extractor, but those cost about $20 bucks per set, and you can buy a new ball valve for less.
Mike