How about a vegetable terrine? The beauty is, you can put nearly anything in them so any recipe can be adapted depending on your preferences. If you're going to make a cold terrine (with goat cheese perhaps), pre-cook the veg in salted water, use the chard to make the outside wrapping and layer away - use plenty of herbs and garlic. The beets will turn things pink but will taste awesome. Cold olive oil tends to set solid, by the way, so if you're serving this from right from the fridge, use canola in the construction and drizzle with EVOO when serving - you'll get the flavour without the "Oh god, grease!" moment. Serve with nice toasty bread and wine.

I'd suggest messing with this acorn squash stew recipe, substituting leeks for the onion or fennel, or adding them in, throwing in the chard (chopped) at the five minute mark, and as you are chopping for the stew, oven roasting the beets and turnips as a side dish.

Acorn stew:

Ingredients:
1 small onion, chopped
6 cloves garlic, minced
1 small fennel bulb, trimmed, cored and thinly sliced
2 cups acorn squash, cut into 3/4 inch pieces
8 ounces Brussels sprouts, trimmed and halved
4 cups vegetable broth, low-sodium or no-salt added
2 tablespoons fresh sage, crushed
1 tablespoon fresh rosemary, crushed or 1 teaspoon dried rosemary, crushed
1 apple, cored and coarsely chopped
6 dried unsulfured apricots, finely chopped
1 1/2 cups cooked red kidney beans or 1 (15 ounce) can-low sodium or no-salt added, drained
1 tablespoon sherry vinegar or balsamic vinegar
freshly ground pepper, to taste

Instructions:

Heat 1/8 cup water in a large pot, add onion and garlic and water saute until tender, about 4 minutes. Add fennel, squash, Brussels sprouts, broth, sage and rosemary. Bring to boiling, reduce heat. Simmer, covered, about 10 minutes or until vegetables are nearly tender.

Add apple and apricots. Cook covered, about 5 minutes more or just until Brussels sprouts are tender. Add beans and vinegar and heat through. Season with pepper.

Oh, golly, what a wonderful haul! I wish I could come over and cook with you.

I love this topsy-turvy stuffed squash [self-link]. It turns the stuffed squash halves upside-down so the hot pan makes the stuffing nice and crusty on top. That recipe is very rich, but because the flavor really comes from the onions and mushroom, it has plenty of room for substitution. I made it a few days ago, substituting vegetable broth for the cream and using a handful of Parmesan instead of all that cheese, and it was smashing good. I don't know that I'll ever add cream again.

In this AskMe thread, I describe how I roast beets and a few ingredients that pair with them. I especially love a spinach or watercress salad with roasted beets and toasted nuts, with or without goat cheese. Mmm, beets.

Here's my favorite simple preparation of chard (or kale or other greens) [self-link again]. You could easily skip the mushrooms. I also often sprinkle cooked chard with toasted slivered nuts or maybe pan-toasted seasoned breadcrumbs --- just a little something to add a pop of texture and contrast.

Thanks guys!
Elsa that chard sounds right up my alley.
I should mention that I have a weird thing where if there are too many different vegetables in one dish, it reminds me of a garbage disposal.
So the terrine sounds like fun but something that I would only add one or two things to, and stews are not my favorite.

Also I am trying to like turnips but so far no luck.
I have roasted them and also made a sweet purée and thought both were gross. Maybe they are just not for me. Is there any way to make them not smell like moldy dirt when you cook them?

Re turnips, my go-to is to treat it like a weird potato and smother it with cheese and garlic in some form. Perhaps make a dry mash, add all the good things (like bacon bits and Parmesan, an egg, a tablespoon of flour)and turn them into croquettes because, you know, FRYING! MAKES! EVERYTHING! BETTER! Serve with a sharp mustard.

Or just a simple mash and gratin? I've also seen a recipe where they were made into string fries and dusted with some sort of herb and chilli salt and served as a beer snack - I haven't made it yet but it might be a good if you like spice. And, possibly, beer.

Chard is also terrific in egg dishes, like as an omelet filling, or in a quiche. Pre-sauteed', of course.

In the fall and winter I have this standby supper that works with any variation of root vegetables and is so easy. Basically, chop your (turnips|parsnips|sweet potatoes|potatoes|squash) into 1-inch dice. You can use just 1 or 2 types or a real variety. Toss everything with olive oil, some minced garlic and onion, and rosemary or other dried herbs, and spread in a baking pan. Bake at 450 for about 40 minutes, stirring often to even out the browned parts. The veggies soften and get roasty on the outside, and it's all very delicious. I make this with pork sausage as an ingredient but you could certainly use vegan sausage or no sausage at all.

Maybe I should ask how I can hide these vegetables in other better food

The shoestring fries sound great! I love spicy things and cheesy things.
I just made a shredded kale and pave and walnut salad, and an Indian chard thing with mustard seeds and a to of cayenne and cumin and I like it.
Still staring at the turnips and squash and beets but thanks to you guys I have some ideas now and my fridge is marginally less shoved to the brim with leaves.

I love parsnips tossed in oil and salt and roasted 'til they're crispy-dark on the edges with other root vegetables. In the winter, I often roast a big pan of carrots, parsnips, potatoes, sweet potatoes, and so on. They're great right out of the oven, but I like to make a huge batch and eat them all week: tucked into cheese sandwiches, scattered over salad with a tart dressing, or just rewarmed over rice. Is it possible that this roasted-together but not-smushed-together way of prepping them would not trigger your garbage-disposal imagery?

I often find pureed or smashed parsnips a bit sweet for my taste, but BOY HOWDY those shoestring fries sound fantastic.

One of my preferences: when I'm serving something sweet (like parsnips or sweet potatoes or a particularly sweet squash dish), I like to pair it on the plate with something darker and earthier (say, mushrooms or beets) and/or something bright and tangy (like chard with lemon or Brussels sprouts in citrus dressing). I love the balance of flavors, and it makes the vegetal sweetness more appealing.

I like to mash turnips together with potatoes. It tends to hide the turnip-y-ness. Plenty of butter/cream/salt.

Beets: I would roast, they are delicious in their own right.

Chard: I would sautee lightly with garlic and olive oil, then serve alongside some white beans and cornbread.

Acorn Squash: Cut in half and scoop out the seeds. You can fill the middle with chopped up apples and cranberries and cinnamon/brown sugar. Or you can just put a little butter and brown sugar in there. Roast at 400 for an hour.