Here's my non-professional opinion. I would suspect that your entire drain system and supply system are in need of total replacement. You can probably do some temporary bandaid first aid to gain some time to prepare, but temporary patching will not cure the problem. Undoubtly your supply system is galvanized pipe which is most certainly corroded to half or less of its original size. As you have recoginzed, the drain system has been patched up before. To deal with the immediate problem, you can try some caulking and see if that will stop the leak. Since drains are not under pressure, sometimes you can get by with something like that. Again, that is the long term answer. One thing about bandaid repairs, if they don't work, you're not out much and you can try something else.