What do I do with these extra multiway wires in my light fixture?
TLDR: Find the ballast.  Cut its #18 white and black power lead halfway down its length, and fit a ballast disconnect there. (don't bother connecting the ballast side). Connect your LEDs on the ballast side of that. 



Since the fixure did not tap into those wires before, you leave them the heck alone.

The irrational need to play with wire groups that are not involved, is the undoing of many lamp projects.  We had one case in an old apartment building where instead of the two wires needed, the asker had dug out a full ten wires from the ceiling, unhooked them all (knocking out the neighbor's power), shot a photo, and asked "how do I hook these back up?"  You don't.  That information was stored in "how they were hooked up before", which the person destroyed.  Now, an electrician has to tone out all those wires and try to figure out what was originally intended. Cost the asker over $300. 

The old ballast has a white and black wire.  The ballast black goes to certain wire(s) in the ceiling. That is where your supply black (hot) goes to.  It doesn't matter what colors they are.  If the wire(s) are white, they must be re-marked with black tape as they are actually hot.  

The ballast white goes to certain other wires in the ceiling, probably white.  That is where your supply white goes to.   You must keep them all together. They're not spares, they're working for a living! 

Really, you should be installing Wago style or Ideal ballast disconnect plugs to the aforementioned wires.  (Not least, it allows you to turn the power back on the moment the disconnect is installed, instead of having to do the whole job in the dark.) However, installing the ballast disconnects will also help you keep the wires straight.