How can I get my family to learn to like healthy food?

Make them eat it for 20 days. Your taste buds are renewed every 20 days and crave whatever you happen to have been eating.

try to make the healthy foods a little more familiar to them. My kids favorite is homemade chicken burgers. buy ground lowfat chicken add an egg and breadcrumbs, shape into patties and coat in seasoned breadcrumbs. bake on a cookie sheet coated in pam at 450 for ten minutes , flip and do the other side for 5. voila, a healthy imposter. I do the same with chicken breasts cut into strips.
figure out the vegetables that they do like and add a new one every few days. slowly they will change their tastes without even realizing.

I started with smoothies, let them create their own. If they are young they will learn by seeing how you eat, it will take time but you will see them starting to make the right choices. Remember they are kids.

My family wants to be healthy and wants to eat healthy... but they don't like healthy foods. They literally would eat burgers all day along with steak if it was up to them. How can I introduce new healthy choices without starving them or being way too overbearing?

Any one have the same problems??

Like many moms, you're don't seem to know what's healthy! A lean steak is extremely healthy if you prepare it right. And hamburgers might not be health food, but they're not junk food by any means (assuming you make them yourself instead of buying them at McDonalds). You can make relatively lean cheeseburgers that taste great They're packed with protein and nutrients. That said, most active kids hardly have to worry about the fat in steak and cheeseburgers anyway. That's more for you and any other adults eating.

The real junk food is the highly processed and/or sugary stuff w/o any nutrients: french fries, cookies, fruit loops, chips, cake, etc.

Now, how to introduce healthier food? In addition to preparing the foods they like in a healthy manner, introduce fruits and veggies wisely. Give them salad, but put some full fat ranch dressing on it (who doesn't like ranch?). Then switch to thousand island dressing, then to oil and vinegar. Even if you can't get them to switch from ranch to other dressings, that's still ten times better than having them not eat veggies at all. Most kids like fruit, so it shouldn't be too hard to get them to eat it. Grapes are cheap and very tasty. If you leave fruits out as snacks, they'll probably get eaten.

Edit: I looked at your profile and noticed that you had kids that played sports. Remember that what's helpful for you to lose weight (low cal) is not what your growing kids who play sports need (assuming they're a normal weight).