It is a delicate balance, to educate without preaching and pushing. My kids are only 10 and 14, but so far are trim and extremely healthy (knock wood). Some of what has been successful has been unconsciously how we engineered the environment in the home (I would highly recommend the book "Mindless Eating" for tips that set you up for success.) For instance, even when we were omnis, I always cooked only small servings of meat, dished out reasonable serving sizes for them, but made huge salads and had those right at the table where it was easy for them to have second helpings.
My kids always like to know the "why" of everything, so I make an effort to educate them about the scientific aspects of nutrition--the benefits of foods that are good choices, the downsides of other options. I try to model healthy eating as much as possible.
At the same time as there is an ideal way to eat, all of us like our "treats". We set it up when we were young that there just isn't candy or chocolate in the home. If they wanted a treat, almost always we would walk to the closest 7-11 and they could get $1 of loose candies. This was actually a stroke of genius, because it required a total of 4 km walk for them to get the junk, gave us time as a family to visit , and gave them the identity of being fit walkers. They are very proud of this. Over the years they have brought many a friend with us, and all the kids love this ritual.
I personally rarely get the candy, and I notice if we are going for our "sev walks" more than twice a week, they will choose of their own accord to buy a bottled water (no calories) or sugar free gum rather than repeated candy.
We used to have a junk cupboard in our home, and you would be horrified to see what we used to keep in it. Now I stock pretzels, rice cakes, crispy minis, dried fruit, and a variety of nuts and seeds. They graze between meals, but keep the quantities very reasonable. They eat fruit as snacks as well, and will cheer to find cut up watermelon or honeydew in the fridge. I make sure to brag about their good eating habits within their earshot and I know this pleases them immensely.
I do a lot of baking as well. You just can't buy the quality of stuff I can do at home. My kid's palates are geared to eating our homemade food and they will often find restaurant or store food too rich. My 14 year old, of course, has a social network that is expanding. Being vegan helps her make better choices, but she will often come home and tell me herself she ate too many chips or cookies. But she notices she doesn't feel well and makes an extra effort to eat well the next few meals. I try not to criticize her choices away, but to discuss some ways she might handle it next time.
Anyway, who knows if anything will stick as they grow up. I was lucky to grow up in a home that was far healthier than most, but wasn't really conscious of the ways to set up a healthy lifestyle for myself and DH. We floundered for many years until I feel we have finally got it right. When they leave home I plan to set them up with a recipe book of their favourite healthy foods, but then it is up to them. Hopefully they won't take as long as DH and I to return to their "roots".