Oni of Blood

Does the Oni of Blood have a power that extends to all of the owning player’s Provinces?
No, the power only affects the Province where the Oni figure is placed. Also, it only compares with other players present in the Province. So, this figure is worth 3 Force in any Province where you have the lowest honor.

What happens when the only player with lower Honor removes their last figure from the Oni of Blood's Province during a Battle?
Nothing changes. The player who had lower Honor may have removed their figures from the Province, but they are still involved in the Battle which stops the Oni of Blood from triggering. Note that if the lower Honour player gained Honor through Seppuku for instance, and then the Oni of Skulls would trigger.