For Odd: The "Superman" moment from The Iron Giant, and he would absolutely own up to it (Though he might not own up to the "Am I A Mistake" song from Mr. Rogers Neighborhood, which he cries just as hard at)

For Jeri, Odd's dad: The Ending of Dead Poet's Society gets him every time, and he's more than open about expressing that (He also cries, just in a more stoic fashion, at the end of The Tale of Iroh from Avatar: The Last Airbender, which he might not be too keen to admitting)

And for Rosemary: She was very much emotionally stunted during most of her adult life, but she remembers crying (and could still feel some faint pang of sadness when she was older) at the animated version of The Little Match Girl (though she'd NEVER admit to it)