Some interesting studies about what children consider "strangers" have been done. The concept is not an easy one for them, apparently, and is very easy to override. For example, in studies, they don't heed the "strangers" warning when the person is clean-cut, a young adult, or, say (in a pretty scary study) someone with a puppy. For this reason, child predators are known to use a puppy, a kitten, or some other enticement as an excuse to lure children (including "can you help me find my puppy?")
There are more practical ways to help your kids avoid potentially dangerous situations than only teaching them about strangers. In fact, teaching them that all strangers are to be avoided eliminates a valuable resource for them if the need arises.
Teach a child to direct adults with questions to other adults (preferably policemen!)
An adult looking for help with anything (including finding their lost puppy) should not legitimately be asking a child or a group of children for help. Teach your kids that adults don't normally ask children they don't know for help, and to simply direct those people to an adult. Practice this with them. For example: "I'm sorry I can't help you. Can you ask (point to the nearest adult) that person to help you?" "Can you call a policeman on your cell phone?" "Can you ask an adult to use their cell phone?" Teach them to look for alternatives to helping an adult they don't themselves.
Give them permission to say "no" to an adult when they feel uncomfortable or confused.
Most parents want their kids to be respectful of adults, and this often means compliant as well. John Walsh of the National Center for Missing and Exploited Children states without a doubt that his child was abducted in part due to this very issue: he taught his child to obey authority without giving him permission to say "no" - to question that "authority" - when that obedience might confuse him.
This includes teaching them to make a lot of noise when an adult tells them to do something they have been taught not to do (go with them, get in the car, etc.)
Instead of teaching kids to avoid all strangers, teach children which types of people they can trust when they need help and you're not with them.
Policemen, store clerks, adults - statistically, especially mothers - with children, etc., are safe people to turn to when they themselves need help (not the other way around; that would violate the first rule.)
Warn them never to accept rides without your permission (by phone or prior arrangement) or a "password".
Many child abductions involve a vehicle. For this reason, we taught our children the concept of a "safe word". We reinforced that we would never send someone to pick them up for any reason without giving that adult the safe word, not even if we were hurt or in an accident, etc. Practice.**
Teach them not to leave a specified area with anyone else without your permission.
Some adults use other children to lure kids. If they're in a playground, they should stay there until they get picked up.
Today with cell phones, it's easier to keep kids safe than when my kids were children. This and the copious good advice found on good child safety websites is a read advantage.
Since this question asks specifically about strangers, I'll limit the answer to that.
Online strangers is a another answer (I think) with a lot of different advice than real-life strangers.
*This last scenario has been repeated often and there are a lot of videos of such mini-experiments available.
**This really proved to be a good one. Someone offered to give our kids a ride home from their play area one day. That they refused because the adult didn't know the safe word was reassuring.
Rethinking “Stranger Danger”
Child Safety Is More Than a Slogan