Do they like spaghetti type sauce? If so make a big batch (or used jarred) and add in veggies like cooked carrots, spinach, zucchini, etc. Then you can blend it all up and they will never know the veggies are in there.
They probably will develop a taste for the sauce like this and when they get older they'll just eat the veggies and you won't have to blend it.
Have you tried things like spinach tortellini, etc? They usually like things like that where they can pick them up easily, or at least my son did.
As for stuff they need to be spoodfed, I say let them go for it. My DS is almost two and can use a spoon and fork just fine but sometimes he just likes to use his hands and has done so m any times with applesauce and yogurt. Messy, yes, but they are toddlers, everything is messy!
If you do oatmeal you can sneak stuff in like canned pumpkin or applesauce and even very small diced fruit or another puree you have.
What about avocados? Those are a favorite here.
Have you tried making the veggies differnt ways with different flavors, etc? Like maybe a little lemon or olive oil or something? What about sweet potatoes just baked with some cinnamon?
One of my DS's faves is red beans and rice, he loves it. So I started steaming mixed veggies and mixing them in for him or sometimes broccoli anad he eats all of it because it tastes all like the red beans and rice.
If you need more ideas let me know I'm just not sure what you have tried and what you haven't.