You can easily win as serial killer, I have several times, just ask my dead wives. oh You can't... ok ask me. Did you ask,"Hey Town Drunk, how can I win as serial killer?"? Pull up the bucket over there and I will throw out my pearls before swine.
As serial killer you are immune to night attacks, this means if someone tells the town you are immune you need to convince them you are the executioner unless he is dead and say second executioner playing in all any mode. Then you need to quickly redirect it back at the plantaphile... the complantmer... the accuser, saying they must be mafioso or godfather, since they attacked you at night. Unfortunately some towns love to hang executioners! I was serial killer in a town and just because of night immunity she got lynched. It worked to my advantage and I won.
Keep your head down in the first part of the game. This means don't talk too much and see which direction people vote. Don't kill right away be random and take nights off. If you see a person who is the first to accuse and votes guilty, then KILL them. They are not a person you want leading the town. In your death note write something cleaver (not porn messages) and then pretend late in the game to be an idiot. Sometimes I make up a list of townies to be killed with my name on it. Example;
My Bucket List Living: Bob Smith, Jim Jones, Town Drunk, Fred Warden, Mary Allen Dead: Frank Wales
But then I killed out of order Jim and the others are still alive change the note to read;
My Bucket List Living: Bob Smith, Town Drunk, Fred Warden, Mary Allen, Harry Nads Dead: Jim Jones, Frank Wales
Leave names off your list to cast suspicion on them. If your serial killer is smart, people will be thinking, Town Drunk can't be the serial killer, he's an idiot!
If people are voting you up to be hung, say something like; "Sure hang me, my target is dead now." That might make them think twice that you were executioner and are now the jester. "Remember only one needs to vote guilty to die." Should top that turd cake with crap frosting on it. Doesn't that make you hungry? Well leave me some loosh change in my tin cup... oh wait I forgot to dump it.