Say I have some hbtdosH005 Goblin horde tokens (15 points each). KH munches on them to get life back as well as the +1. (and only +1 since the rulling in this thread)

how would the scoring work on these guys?

I know in the old rules, it used to be that the points were split evenly between all players if none had damaged it and if it was KO by the controlling players actions (Pushed to death, Energy Explosion, Pulse Wave, etc).
I found this on page 17.
So, if KH is munching down these tokens, your opponent get full points for them now?

In a game with more than two players, do you get a portion of them, or does it only go to your opponent?

Page 17 of the RB:

Defeated characters. Every opposing character that is defeated during the game earns you a number of victory points equal to its point value.

And that's it. Doesn't specify which player does the defeating or how it was defeated, just that it was defeated.

So each time King Hyperion KOs a friendly character, that may help Hyperion, but it is also points in the bank for the opponent.

As far as multiple player games... well, you've got it all written right there. Depending on the conditions, maybe one player gets the points, maybe all your opponents get to split the points.

Wasn't there something in the rules at one time (in reference to multiplayer games) that said which ever player last damaged that figure got credit for the kill and thus the victory points?

Or maybe I am just remembering a house rule or something...

At one time? It's still there (and, to the best of my knowledge, has never left):

When playing with more than 2 players, victory points from defeated characters or removed objects go to the player who was active when the character was defeated. If a character was defeated on its owner’s turn, the opponent that has most recently damaged the character earns the points. If no opponents damaged the character, the points are divided evenly.

So, like I said, depending on the conditions, maybe one player gets the points, maybe all your opponents get to split the points.