CATERING to the vehement food likes and dislikes of children and teen-agers is hard enough in a family. Multiplied several hundredfold, the task seems insurmountable. Making institutional food taste good is admittedly difficult. The task is almost impossible when the institution is a school where money is limited; the time for eating is short - sometimes 20 minutes; the lunchrooms are often dreary, and educators treat the lunch hour as the least important part of the day.

Despite such problems, some school lunches have been improving, starting in the mid-1970's, when the country's nutrition consciousness was raised. That set the stage for a new type of school food-service director, one committed to getting a healthful, appealing meal into the students instead of the garbage.

Croissants and taco salads, French bread pizzas and nachos with cheese - these and other attractions from the nation's fast-food restaurants can now be found in some of the country's most innovative school lunch programs. Not that they have replaced the fish sticks and beef stew that millions of children love to hate. Rather, they have added a variety to the menus that have some youngsters admitting they like school lunch.

Over the last few weeks visits were made to five schools - three in New York and one each in Newark and Fairfax County, Va. - where lunch programs have won parental approval and, at least, grudging student acceptance. The efforts of their food directors have been twofold: to upgrade the nutritional content of meals and to make them more appealing.

Some nutritional improvements have been fairly easy. Many dishes can be prepared with reduced salt, sugar and fat without attracting attention. Where change has been noticeable, students generally have adjusted. ''With the institution of lower salt and sugar in the junior high five years ago, by the time the children get to high school, they are attuned to it,'' said Lorraine Nardi, school lunch manager at Forest Hills High School in Queens.

Establishing nutritional balance to school meals has also been a realizable goal. For example, Fairfax County, whose student population has held steady at about 109,000, purchased 54,000 pounds of salad greens in 1977; last year, it bought 123,500 pounds of greens. Over the same six-year period, broccoli purchases went from zero to 1,900 bunches. Meanwhile, butter consumption dropped 75 percent and sugar consumption 71 percent. (There are no figures available for New York and New Jersey.) Making school food more palatable, however, has required unusual inventiveness and a little psychology. The more successful program directors have brought variety to their menus and students into the food selection process. Visits to the five schools indicate that these tactics have had some success. Student griping continues and there are still plenty of children who eat only cookies, but food-service directors say that more food is being eaten and less thrown away. The revision in Federal school lunch regulations known as ''offer versus serve'' is one reason why. Under the new regulations, which became fully effective in 1982, children are not required to take the five items on the federally mandated school lunch; they need only choose three.

Elizabeth Cagan, who retired this year as director of the New York City school lunch program, was one of the first to take advantage of the new rules and the new school lunch climate. She insisted that foods sold to schools meet nutritional standards. She widened menu choices and introduced nutrition education.

The classes are the program's most important feature, said Barbara Friedlander Meyer, who is the city's nutrition education coordinator. Children will eat the right food, she said, ''if it's tasty and appealing and if they become better-educated consumers.'' The same philosophy holds true in Newark, where Bernice E. Mayes, the director of school food- service programs, said that if she received more Federal aid, she would establish nutrition centers, since training would ''rub off on the next generation.''

Not all school food-service directors agree. Dorothy VanEgmond- Pannell, whose Fairfax County program is given high marks by fellow directors, recalled giving students intensive nutrition education. ''It did not change their habits,'' she said. ''We've tried about everything there is, and our conclusion is that we just have to wait until they get older.''

The goal of all school lunch programs is getting nutritious foods into students' stomachs. In Fairfax, Mrs. Pannell said, ''We'll do it however we can.'' At Brearley, a private school in Manhattan, that meant hiring Joseph Civita as food-service director. When he arrived in 1976, he immediately did away with the school's convenience-food offerings. Mr. Civita, who trained at New York City Technical College and in some of New York's better restaurants, including the Four Seasons, said, ''If you put out good, fresh food, good nutrition will follow.''

Private schools do not have to comply with Federal regulations for school lunches or rely on surplus commodities, so they have more leeway in their lunch programs. This does not necessarily translate into superior meals. As 14-year-old Vanessa Houghtlan of Brearley noted: ''You go to other schools and say 'Where's the salad bar? Where's the fresh fruit?' All they've got is hot dogs.''