Culture as a weapon

Culture doesn't seem to do much in quick multiplayer games online but in these long multistar games it's critical. I've taken to setting up 4 advent starbases in the star grav wells of systems I plan on taking eventually. After upgrading them to 2 culture and 4 hangars I find the culture softens up the star system dramatically and 80 bombers in a star grav well can take out entire fleets so they're well protected. By the time I get a fleet there the culture has usually squezed out almost all of the enemy culture and caused most planents in one or two jumps to revolt.

There was one time when I had culture actually migrate from star to star but I have yet to be able to replicate that.

You've hit the nail on the head for the best ways to use culture - combat bonuses and depriving enemies of colonization.  It should be noted, however, that your culture can be negated if enemy capital ships occupy a gravity well for long enough, and eventually they will be able to colonize it.  This can also make it very difficult to use offensive culture if an enemy fleet is defending your target system.

That said, culture/novalith isn't as smooth a combo.  The AI will often lay low and raise its defenses in the late game, avoiding a direct confrontation with your fleet.  This leads to long protracted sieges that favour superweapons, but assures their ultimate defeat.  Against a smarter opponent, they'll prefer to force a battle to try and change the direction of the game, so it typically doesn't last long enough for culture to build up to "game-winning" levels, and superweapons also force them out of hiding, making a cultural offensive less necessary.

I won a small map game with culture playing as Advent.  Granted I jumped ahead to the star (which was the choke point of the map) and set up several starbases; got a few deliverance engines.  That's pretty much all it took.  My culture swept through the AI's empire of 4 or 5 planets and ate away at allegiance until they all succumed.

Of course the game was already decided way before that point and it was me just messing around.  But it surely shows there are other ways to win than a military victory.

(yes I know it wouldn't work as well in MP lol)

As long as you play Advent aganst the AI theres an evil little trick you can pull.  Just get a forward-ish planet (this is late game by necessity) and build 6-7 culture centers depending on how many the planet supports.  Build them in a circle and drop a starbase in the middle, surround them with beam turrets (with synergy), 2 hangar defenses, 2 repair bays and youre golden.  Nothing short of a full fleet can kill this thing and with culture upgrades it pumps out a good 39-42 culture per second.  Nothing can stand up to that, I killed off an Unfair AI earlier with this. 

There's also a research (as a TEC) that gives u 4 logical slot on EVERY system u got (i think its a lvl 5 or 6 research). So even the DEAD asteroide and the ''So well Placed'' Pirate base can build a Broadcast and they can be Easely defended.