One thing I can safely say is NOT a good idea is to try to run a large game with way more people (10-15) than is realistically possible. I know this from personal experience. The horrors I've endured...
On a more 'ideas that might actually work' note, improv games might be a good idea: completely freeform, very short time limits, and with a constantly changing group. From my recollections of high school drama, there's one idea in particular I'd suggest.
It involves a constantly rotating group that the entire 15-25 people cycle through in the space of less than half an hour. You choose three or four people at random and set up a random scenario ('set up' as in 'give one sentence of background fluff'. For example, you choose four random people and say 'You've just stolen the Evil Wizard's Majickal Tome of Pastrymancy and he sicced his strudel-golems on you. You're on the top floor of his tower. What do you do?') and then let them have at it for one or two minutes. Don't let them pause to deliberate: force them to just do stuff. Keep it light-hearted and fast-paced and they'll get used to talking to each other.
THEN once the minute is up, choose one person to be replaced and pull another random (or volunteer) player up to join. After another minute, cycle out the second person of the original four. Then the third, then the fourth, then the first new player, and so on.
Also, remember the golden rule of improv in this: 'yes, and...'. Because the PCs won't have stats or attributes, you can't say no and justify it by the rules, and the players will get butthurt if you say no outright to their ridiculous shenanigans.