The quickest and easiest way to fix many holes in cast iron drain pipes is to surround the hole with silicon caulk, wrap the pipe with rubber gasket material, and clamp it with hose clamps. But that simple fix won't work when the hole is in the bends of a tee joint, because a flat piece of rubber won't cover the hole. In that case, it's best to cut out the damaged pipe and replace it with new PVC pipe.
Secure all existing pipes to the wall with metal strapping. (Heavy iron pipes can slip and fall when you remove supporting tees). Cut through all three iron pipes with a saw or grinder and diamond bit blade, a few inches away from the existing tee. Remove the tee.
Cut one piece of PVC pipe for each of the three joints in the PVC tee, making them longer than the old iron pipe that you removed. Prime and glue each piece into the tee. Set aside to dry.
Slide rubber couplings onto the end of each of the three iron pipes, pushing them all the way onto the pipe.
Hold the PVC tee up to the place where the iron tee was removed. Mark the ends of the PVC pipes where they need to be cut, allowing a ¼- to ½-inch gap for the three junctions. Cut the PVC pipe at those marks.
Hold the PVC tee in place and slide each rubber coupling midway between the PVC and iron pipes. Tighten the clamps with a screwdriver. Test the tee for leaks.
Metal-cutting blades will not work with old iron pipes, because they are incredibly hard. Only diamond blades will do.