Next of Kin (Oblivion)

Background
Your objective is to eliminate the entire Draconis family, five targets in total. The only information you have to start with on this mission is the location of Perennia Draconis, the mother of the doomed family. She is located at Applewatch farm just west of Bruma.

Perennia Draconis
Head to Applewatch and speak to her. You must extract the location of her children and then kill her. The best way to do this is to pretend to be the shopping service she has hired to send gifts to all her kids. She'll generously give you a list of all the other Draconis family members as well as 100 gold for the errand. Kill her and then move on. You could also kill her and take the list from her or let an enemy kill her. If you have not completed the main quest line, it is possible that an Oblivion Gate will have spawned nearby. You can lure any number of enemies from here to kill her.

Caelia Draconis
Caelia Draconis is a city watch guard in Leyawiin who works the night patrol. Unfortunately, she doesn't appear to have any moment of vulnerability you can exploit. She is rarely alone and is always armoured. Any attack in public will of course leave you with a large bounty, not to mention a great deal of trouble from the other Leyawiin guards. The best time to take Caelia out is just after she finishes her watch at 7 am. She will go to a private room upstairs in the Three Sisters Inn. Here it is possible to engage her one on one. A one shot kill here is difficult due to her being fully armoured so you will likely pick up a small bounty regardless. One way of avoiding the full 1000 gold whammy is to whittle her health down to a small sliver and then use a poison attack with a long duration. Do your best to avoid her until she succumbs to the poison. This death should only leave you with the 40 gold bounty you picked up for the initial attack.

Andreas Draconis
Andreas is located at The Drunken Dragon Inn and always has a guard posted in his room, staring almost directly at him, at all times, with no breaks. This makes it almost impossible to simply kill him. However, there are several ways to trick him into attacking you, at which point you can defend yourself. Simply talking to him and either saying that his mother bled like a pig or that you would like to kill him is the most direct way. If you tell him his mother bled like a pig, he gets mad and attacks you, at which point the guard attacks and eventually kills him. You can also use a Frenzy spell. Should either of these count as a crime in any way, try lowering his disposition to 0. (Enter the Speechcraft minigame, and either deliberately fail at it by matching the large wedges to the options he hates, or simply not pick anything and stare blankly at him as his disposition slowly falls.) He is very aggressive, and will attack you simply for not liking you.

While the constant guard presence makes him almost impossible to assault without an alarm, the guard proves to be his undoing if you get him to attack first, arguably making this the easiest kill in the entire mission.

Another way of killing him is to wait until he is asleep, and then perform a sneak attack for a one-hit death, behind the counter. If done correctly, the guard will not see you and you will receive no bounty.

Yet another way is to simply sneak to the steps behind the guard, arm yourself with a good bow, poison your arrow with a paralyze/damage health poison and shoot the guy. This will knock him out and he will die quietly. The guard will do nothing as long as you remain in sneak mode.

One more way to do this is that if you have a charm spell for ~100, just charm the guard and then stealth kill Andreas with an enchanted dagger, such as the one given as a bonus from the Brotherhood. The guard will run over to you but since the last of the damage was done by the dagger and not you, it's only an assault and he lets you off without a bounty.

You can also break into his room, tell him you are going to kill him, run to your guild, but make sure he is chasing you. Your guild will kill him and you will have no bounty. I just tried for over an hour to kill him and this was the only thing that worked for me. I ran to the mages guild and ran from him.

Sibylla Draconis
Sibylla Draconis lives in Muck Valley Cavern with her surrogate family of wild animals. This kill is straightforward and you should approach it like a standard dungeon crawl with a boss. There are no witnesses other than her mangy (and probably dead) crew, and since she is aggressive and will attack you on sight, you don't have to worry about any nasty bounty this time.

In the first cavern you will confronted by a wolf and a rat, the second cavern contains 3 rats and the last cavern contains Sibylaa Draconis herself, accompanied by 2 rats. This is level dependent, as a level 12+ you have to kill black bears.

Its possible that once you enter Muck Valley Cavern you will see her standing right in front of you with her back facing towards you making this a very easy kill

Matthias Draconis
The final family member can be found in the Talos Plaza District of Imperial City. Matthias Draconis is asleep upstairs in his house from 12 am - 5 am. Pick the lock to his door and end him.

This can sometimes be very difficult if there is another NPC walking around downstairs, but if you have a very high sneak (or possibly chameleon spells) and he is facing away from the door when you walk in, you can sometimes sneak up the stairs to where Matthias is without being spotted.

If he is not in his house, Matthias works as a Guard in the Umbacano Manor, you can find him in the basement. Easy to kill, a way to not get a bounty if a guard is nearby is to tell him you killed his mother he will become aggressive and the guard will kill him for you. If he is outside of the manor, follow him until he goes through a stonewalled garden, here you can sneak attack him with no bounty.

He may also be found at The Bloated Float in the Waterfront.

NOTE: Killing Matthias during the Adarjhi's Heirloom quest will get you kicked out of the the Thieves Guild and you will have to pay the blood price.

Pick up your reward and new orders at the next dead drop in Skingrad Castle courtyard.

Please note that you can kill them before this quest so as soon as you get it, you will finish it.

Trivia

 * Andreas Draconis of the Drunken Dragon Inn suggests that you go to the Inn of Ill Omen or the Tiber Septim Hotel instead. Both of those inns are involved with a Dark Brotherhood quest.
 * If you return to Applewatch sometime after completing the quest, you will find the tombstones of all five Draconis members, with a personalized epitath for each, and Caelia's sword leaning against hers. If you read Perennia's headstone, its epitath is somewhat threatening ("Here lies Perennia Draconis -- May her spirit forever curse the murderer who stole her precious life") and reading it causes her ghost to spawn directly behind you and attack. The ghost is extremely weak and should not pose a threat, but it can be startling. (Or it might just blatantly scare you).