Time to re-address this old question.
When it comes to removing Tasks (not Quests, but repeatable Tasks) in your Quest Log that won't go away, you can remove them by killing the NPC who owns the task!
Press H to enter aggressive mode and kill the NPC you are supposed to talk to when completing the Task. Then fast-travel or fight your way out to a place you can fast-travel, and head to an Inn or your stash house. After sleeping for 3+ days all crimes will be forgotten and you can return to the area.
Sometimes aggressive mode doesn't want to activate so just spam the H key while attacking and you'll get it.
As for accidentally killing important NPCs, I think the game resets the necessary ones but you can definitely permanently kill some NPCs that have unique names. So be careful!
When I found this out I went and cleaned up my task log, because I hate clutter! Go kill those annoying non-task-rewarding NPC losers and get your Quest Log back in shape!!