There are several excellent sites that allow students to easily and quickly make animated films. The best one is D.Film Moviemaker, and you can see many examples of films my students have made using this online application under the Student Movies category of the Examples of Student Work page. The creators of this site have also announced that a new version will be released soon.
Under the same category you can find other links to sites that allow you to make online movies. My students haven’t tried those yet, but they, too, look easy enough for English Language Learners to use.