Hardly a moment passes in ''Anastasia,'' 20th Century Fox's splashy foray into the Disney-ruled sweepstakes of the animated musical, when you don't have the queasy feeling that a nervous corporate committee was breathing down the neck of this unfortunate movie, forcing it to be all things to all people no matter what had to be sacrificed in elementary common sense.
All things means, in this case, a hybrid of ''Cinderella'' and ''The Wizard of Oz,'' done up in the glossy look of a Disney film. It means surrounding the main characters with lots of chirpy critters wherever they go. It also means throwing in some animated action-adventure sequences, of which the most spectacular is an exploding train wreck, and sweetening the story with some generic pop songs by Lynn Ahrens (lyrics) and Stephen Flaherty (music) that don't quite measure up to Celine Dion's Disney hits.
But most of all it means adapting Russian characters from a 1956 movie that starred Ingrid Bergman and Yul Brynner into bland all-American types who look and talk like San Fernando Valley teen-agers. Judging from their voices, about as close to Europe as most of these characters have ever gotten is probably Fresno.