Chocolate and strawberry milk are out. Next to go: Corn dogs and chicken nuggets. The Los Angeles Unified School District on Tuesday, with a 5-2 vote on a new dairy contract, became by far the largest district in the country to remove flavored milk from its menus, part of its effort to make school food healthier and help combat childhood obesity. The milk issue has overshadowed other changes in the district’s food services division, which serves 650,000 meals a day at 1,000 sites. A menu overhaul is underway that will mean fewer meals that resemble fast food and more vegetarian offerings. Spinach tortellini in butternut squash sauce and California sushi rolls, along with many ethnic foods, are to be added. Corn dogs, chicken nuggets and other breaded items are out, said Dennis Barrett, food services director.