Saturday Night Dinner West LA for 16
Musha might be a bit pricier, but worth it, esp if you get the back room.
Papa Cristo's for Greek might be able to work out a family style menu for you.
Maybe somewhere for shareable plates like Zu Robata
You might also consider some Sawtelle places... call ahead and see who can accommodate... Orris (likely tight), Hurry Curry, or Ramen...
If you want to go farther east, you could do Ethiopian on Fairfax.
There is NO WAY you do acceptable sushi for less than $20 per person. Are you thinking that everyone would order their own entree? Or more a collection of dishes that everyone would share? Are you including beverage and tip and tax in that under $20? Alcohol??? Is everyone paying separately or are you footing the bill?
With shared dishes spread among maybe two or three tables, I'd say look at the menu for Shamshiri (Persian -- kabobs, stews, rice) or Hu's (Chinese -- soup and spring rolls or dumplings, plus a variety of entrees) or maybe taking over a portion of a place like the Shack (burgers, sandwiches, bar bites and beer).