I have an idea for a new character - a psychotic, homicidal maniac who believes all the Jarls want him dead, so he decides to kill them all first. But is it possible to kill them? I realise it'll probably need pushing up the sneak and a combat skill level/perk trees.

Has anyone tried killing them all?

With mods I know it's possible.

I have never tried to kill a jarl really. But I think they are. some might be set to essential before certain quests are finished.

Yes, all Jarls are marked as essential in the game, so you can't kill them by normal means. The only exception of course being Ulfric during the Battle of Windhelm (if you choose that route in the CW).

If you're playing on computer, you can use the mod "Sneak Tools" which will let you kill essential NPCs.