Hi there
it is more correct to say "Eating and drinking in moderation will help protect you from dangerous diseases."
We don't "stay " away from the kind of diseases that are brought on by unhealthy eating and drinking, we can "protect" ourselves against the diseases though, through sensible habits etc.
We can "stay" away from contagious people who might have the kind of disease that can be spread through human contact
Deborah ESL