I adore veggies. Here are some tips, in no particular order:
1. Spinach goes great in lasagna. It won't take over the entire dish unless you go totally crazy. You can cook your own, or thaw some frozen. Either way, make sure you chop it well and squeeze as much water out of it as you can. Mushrooms are also good in lasagna (just saute some minced ones in oil and mix in with the sauce or meat). Paper-thin bell peppers can be delicious, but the green ones will be detectable.
2. For green beans, asparagus, zucchini spears, and okra: Clean and trim the veggies. Dice a tomato or two (you want about one part tomato to three parts green stuff) and mince up a clove or two of garlic. Put the tomato and its juices into a bowl with the garlic and season with a bit of salt and pepper. Heat a tablespoon or so of olive oil in a large skillet over medium to medium high heat. Toss in the green veggies. Cook over this high-ish heat for about four to five minutes, tossing them around with a spoon. A few brownish spots are fine, but you don't want them to be getting soft. Turn the heat down to low, push all of the veggies together (stacking is fine), and top with the tomatoes and garlic. Don't stir. Cover the skillet and let it cook over low heat for about fifteen minutes. Take the lid off, and give it a stir. The tomatoes and veggies will probably have released some juices. Turn the heat up to medium again and let it bubble and thicken. When the veggies are done to your liking, serve them. Or just eat them out of the pan.
3. You've already had the roasting tip. Roasting is fabulous for root vegetables in particular. I like to make a hash out of potato, sweet potato, carrot, and beet. I just peel them, cut them into 1/4-inch cubes, then toss with a chopped onion (if I have one), some balsamic vinegar, soy sauce, olive oil, salt, and pepper. I might toss in some fresh thyme or rosemary as well. I put it onto a baking sheet and toss it in the oven. It will cook at most temperatures, though it does take longer at lower temperatures. Give it a stir every ten minutes or so after the first fifteen minutes. I'd suggest 375 degrees. It's nice on its own, with gravy of some sort, or pureed into a soup.
4. People have already suggested the Sneaky Chef books. Great idea. Try it out if you can find a cookbook at the library.
5. If texture is a big thing for you, experiment with different cooking times. Take, for instance, zucchini. Raw, it has a slight "squeak" to it. It also has a faint "green" flavor. It's almost grassy sometimes. The more you cook it, the more tender it becomes. To you, that might read as waterlogged or slimy. Keeping it firm might be a better choice if you are sensitive to texture.
6. Try roasting some veggies with a breadcrumb topping. I've had good luck with Brussels sprouts that way. I blanched them briefly, then put them into a casserole and topped them with breadcrumbs that I'd whirled with almonds, lemon zest, salt, and pepper. I drizzled olive oil and the lemon's juice all over the top. It was quite refreshing, but it did taste distinctly of Brussels sprouts.
7. Do you like curry? Curry is amenable to many additions. You can cook it until it's almost done (blanching is easy), then dump it into your curry and let it finish cooking as it bubbles in the sauce.