Hi Toni! Welcome to Big Paws Only! Even though your dogs aren't as hefty as the rest, their size makes them as welcome as the rest.
I am glad that you have found a breed you really enjoy. I have heard that retired Greyhounds do make great pets!
I have not had any personal experience with them, but I can offer a piece of advice with the biting problem. First, I completely agree with you about causing more pain or allowing aggression- even if it is just to "put him in his place". Since yelling "no" and "ouch" don't work you may want to try an attention getting method. Get a small, metal juice can (apple juice or something) and put a few pennies in it. Cover the top with tape and then shake this rattle can whenever Oz does something bad. It is loud and will stop any behavior at that moment. Once you have the dog's attention you can begin to correct the problem. And since you said that putting him in the backyard did work, you may try that too. I know that with my Bear, outside punishment is the worst. Good Luck and keep us posted on how the rattle can works!