Where to have lunch in Santa Cruz?
O'Mei would probably accommodate such a group, and indeed many people really like it. I'm not one of them, though. I feel like they're neither authentic "Regional Szechwan cuisine" as claimed - the spicing is nowhere close - nor are they a fusion restaurant that many seem to think they are. I can best wrap my head around it as "O'Mei is to Sichuan food as Americanized Chinese food is to Cantonese food". In other words, a legitimate style reinterpreted for the taste buds of non-Chinese people. Not my cup of tea, but I may be in the minority.
In my experience, having 20 people converge on a decent sit-down restaurant means that you'll end up with a more limited menu, so it might be tough to satisfy the variety requirement with such a group. But maybe in such economic times, you'll be given more leeway.
That said, here are some suggestions: if you want Asian, the best place that comes to mind is Shun Feng. Could most likely serve up some banquet-style deal with a bit of notice. For Mexican, many of the more hole-in-the-wall places that I prefer (e.g. La Cabana) are probably too small to handle such a large group. For bigger places, maybe El Palomar downtown can fit you? I'm not terribly enamored with their food, though. For Italian, Avanti doesn't do lunch on weekends (I'm assuming it's a weekend but maybe that's a bad assumption) and even if a weekday, is probably a bit on the small side. La Posta doesn't do lunch. Also on the small side is Limoncello which is also quite decent, with same no-weekend lunch problem.
Sorry I'm not being too helpful. The intersection of sufficient space, good food and lunch doesn't seem to be a very big one. Removing cuisine requirements, I'd look into Hula's downtown. Their website says "The Tiki Room is also available during lunch hoursfor private parties. Seating up to 50 people." Hawaiian-ish food that's decent, not great but definitely serviceable.
Personally, I'd order a pile of sandwiches and go have a picnic down at the beach or in the redwoods but that might not be an option for you. Otherwise, I think Shun Feng may be your best bet.