Las Galas has all of those you mentioned... just talk to the owner (David) and he can pretty much come up with whatever your needs are. They deliver if you're within the vicinity so you may need to check with that. But overall they give you a gang-load of food with the best bang for the buck. I recommend their Chinese Chicken Salad (hands down the best in Little Tokyo), Teriyaki Chicken and Shrimp Yaki Soba
103 Japanese Village Plz Mall
Los Angeles, CA 90012
Check out Reikai's Kitchen. I think catering is how this place started out. They do catering for events in Little Tokyo. They occupy the former dining room of the Tokyo Towers apartments in Little Tokyo.
455 E. Third St. (San Pedro St.)
Los Angeles, CA 90013