Coincidentally, another site that I'm on started its own version of an online Clue game just a couple of days ago, so maybe their setup might help with some inspiration.
The game there is being run with teams of 3-4 people, and the culprit (a thief rather than a murderer) is an NPC, so to speak. That isn't very Mafia-esque, of course, but it fits all right with the Clue theme. There's a virtual deck of cards, and as in Clue, one card from each category has been removed to choose the thief, method, item stolen, etc., randomly. The remaining cards have been numbered.
Each round features a new puzzle to solve, a word game, trivia questions, etc., and each team that gets the correct answer chooses a card by number, thus eliminating one possibility. Every third round, there's an extra bonus -- each team chooses another team to question. They make a suggestion, choosing one item from each category, and if the team being questioned has drawn any cards that disprove any of the items, the team doing the questioning gets to see them.
The puzzle aspect isn't very suited to Mafia, of course, but that could just as easily be that each remaining player chooses a card each round, something like that. Or perhaps the cards are hidden around the rooms, and anyone searching a room that still has hidden cards has a certain base chance to find one each round.
The other game has a lot more options than standard Clue, featuring a thief, an accomplice, the item stolen, how the thief escaped, and where the item is now hidden, with eight in each category, so obviously it takes a while to find out everything.
There are also some non-standard cards included, like a Trapdoor card that causes you to lose a turn, an Eagle Eye card that lets you choose two cards next round, and other such things, to help shake the game up. If you decide to keep the murderer setup as it is, that might be another way to help even things out. Or maybe the murderer could set traps to kill at a distance, thus helping to disguise that person's identity.
We're only three rounds in, so about all I can say at this point is that it seems to be working out well so far, and it looks like an interesting take on the game. :)