To get to the Stray Demon, you will need to return to the Undead Asylum. When you get to the area where you fought the Asylum Demon, the floor will break away and you'll drop down to the area with the Stray Demon (and you'll lose some health if you don't have Fall Control). This boss is quite similar to the Asylum Demon, except it has a lot of health and one attack that stands out from the rest. It will slam its axe into the ground, causing a large explosion in front of him, as well as small area behind him. You should be able to get 2 good hits on him (3 if using a quicker weapon) after this attack, and then you should retreat after. Your best bet is to stay behind the Stray Demon and don't be too far away from him. Just remember to not be too greedy with your hits and always keep your health high, because if you get hit by his shockwave, it will hurt.