you could make pickled red onions:
http://orangette.blogspot.com/2006/07/proper-pickle.html

or an onion based pasta sauce (no regrets at ALL on this one, it's fantastic). It's the first thing that came to mind when you mentioned onions. In fact, I think I'll be making it tonight. Take your time with the onions, they'll be much better if you do.

http://orangette.blogspot.com/2008/05/entirely-unmannerly.html

French Onion Soup. Would dicing and freezing work?

Chop/dice them, freeze them flat on a cookie sheet for an hour or so, then place them in a freezer baggie or something of that nature.

When you aren't getting as many in your CSA box and want to use onions in dinner, grab a handful of the chopped onions, toss them in the pan and they cook up wonderfully.

Oh, I should mention that for the pasta recipe I posted, a mandoline is a really nice thing to use. If you don't have one, try refrigerating your onions for an hour or so before you cut them. If they're cold, the volitile oils that make you cry aren't quite so bad. Even so, I always end up looking like a really bad breakup after cutting that many onions.

All great suggestions! I will certainly put a lot of these to use this week.

Thank you!

I second caramelized onions. You can store and use them in anything (sandwiches, pasta, salads, pizza, casseroles, etc.). You could also make a nice chutney with onions and mango - can it and preserve it and give em away as gifts!

I was going to suggest onion pickle too, see Tiamat_The_Red's comment.

Look for indian recipes. Many will use a whole onion for a single dish. My S.O. is indian and we cook indian at least once a week, that mixxed in with western cooking we easily use 2-3 onions a week. I never leave the market without an onion or two, i figure ill need it soon enough. An easy, quick, and healthy favorite of mine is chana masala (curried chickpeas), good way to use an onion!

http://www.recipezaar.com/Indian-Chana-Masala-266068

Or make an onion chutney to serve over rice, with flat breads, even on sandwiches etc.

http://www.indianchild.com/Recipes/chutneys_recipe/onion_chutney_recipe.htm

Recipezaar.com has some other good looking onion chutney recipes.

http://www.recipezaar.com/Killer-Onion-Chutney-12952

Freezing caramelized onions is a great idea. You could thaw and put on pizza, in a frittata, etc.

But french onion soup is too delicious to skip. I made this one last fall with lamb stock I made from bones from 3-Corner Field Farm at the Union Square Greenmarket.

http://www.pithyandcleaver.com/?p=46

p.s. not cooking related but... if you plant an onion you will get a lovely flower eventually!

http://upload.wikimedia.org/wikipedia/commons/thumb/6/63/Onion_Flower_Head.jpg/300px-Onion_Flower_Head.jpg

How about this onion jam recipe:

Roasted Garlic and Onion Jam

3 large Spanish onions
2 heads garlic - roasted
2 tablespoons sugar
2 tablespoons brown sugar
4 tablespoons balsamic vinegar

Squeeze roasted garlic cloves unto a small plate. Set aside. Cut onions in
half lengthwise; peel. Cut off ends; cut lengthwise into 1/4-inch thick
pieces. Coat a 13 inch skillet with cooking spray, and set over medium heat.
Add onions, and cover. Cook, stirring occasionally, until softened and
translucent, about 15 minutes.

Add sugars; recover. Cook, stirring occasionally, until onions are golden, 20 - 30 minutes. Add 1/4 cup water and stir. Cover and cook until dark brown, 20 -30 minutes. Add balsamic vinegar, roasted garlic cloves, and another 1/4 cup water. Continue cooking until liquid has been absorbed, about 10 minutes. Transfer to a bowl to cool. Store in an airtight container in the refrigerator for up to 1 week.

Courtesy of Chowhound user Atlantis here.

I know this is so wrong, but... refrigeration! Seriously, I always stored onions outside the fridge, but ended up turning to it in desperation when i had a surplus, and it worked out quite well - they can live in there for months!

Make onion jam, which is basically pureed caramelized onions. It reduces a heap of onions to practically nothing (but such a delicious nothing!).

Seriously getting a middle eastern or turkish or armenian cook book, everything has at least an onion in it, and their basic stews are really simple to make. There's a turkish dish that comes to mind, because of its heavy onion use. I think you could use all three. Its basically eggplants, peppers, onions, and garlic and its amazing, its called imam bayildi. (oh cook the eggplant in the oven to lower the fat.)

i chop and freeze onions all the time.

Indian food! there are tons of yellow onions in it. I made aloo ghobi last week and used up 3 onions. Then you can freeze the leftovers and have a bunch of lunches for another day.

Is there something wrong with me that I go through about 5 onions a week? I buy the big mesh bags full of onions and never have to throw any away, or freeze them, or make jam. I should probably invest in breath mints.

This is the best recipe for French Onion Soup.

http://www.foodnetwork.com/recipes/tyler-florence/french-onion-soup-recipe2/index.html

Forthright Fattie, I go through a LOT of onions too. One a week? More like one a night. ;)

In a Lora Brody slower cooker cookbook recipe I have you put whole onions, low sodium chicken stock and butter in your slower cooker and cook on low for 24 hours. The aroma will drive you insane. After that you can freeze them for french onion soup. And after chilling you can separate the butter and have onion-infused butter for baked potatoes, etc

I grill the whole onion when bbqing. then pull the layers apart and add them to tacos or scoop salsa with them (and place in your mouth quickly!).

a texas thing?

I choose the driest and firmest onions that are intact in complete skins, wrap them in newspaper individually, and store them in a cool dry place. The onions that clearly need to be used immediately (they have a nick through the outer paper exposing the onion flesh or are moist or need to be trimmed), those I caramelize and freeze, then I just add a bit of onion flavor to a dish whenever it's appropriate. One trick I like to use is to add just a few drops of balsamic vinegar at the end of cooking... makes really great sweet/sour onions (perfect in pasta dishes or on sandwiches). And if you grow onions yourself, like I do, they keep in the ground for a very long time so I try to store as many that way as I possibly can.

Make Pissaladiere or Alsation Onion Tart. Now!:)

http://www.lemontart.typepad.com/

At our house sometimes we like more of the onion flavor versus actual pieces of onion. When we buy big bags of onions we take some of them-peel them, run them through the food processor and really pulverize them..then freeze them in an ice cube tray. Once frozen we put them into ziplocs and keep them in the freezer..each cube averages about 1/2 an onion..and you can use it in whatever you'd like! Sauces, stocks, etc! Hope that helps!

How big are these onions? Using them every day and yet only going through one a week doesn't quite add up to me. We're only 2 people and I'd say we go through 5-7 onions on an average week and it isn't as though we are onion-crazed. I'd suggest just upping the amount of onion in whatever you are making now, it can't be much. Also, if you store them properly, they should last a couple of months--well into the time your CSA should be giving you something beyond onions.

I rarely have enough onions to do this since I go through a lot of onions. My grandmother cuts the legs off pantyhose and hangs onions up in a cool spot of the basement with a knot between each onion. When she wants one she just cuts the bottom most knot and takes the onion out. She can store them for months that way. If you don't have a basement an out of the way closet will work too as long as it's dry and doesn't get too hot.

I'm with Rachel. We're two people (my housemate and I) and we go through 7 or so onions a week. I chop them and put them in everything.

A few things that you might consider:
Onion soup
Onion tart
Do a stir fry with onions and garlic and broccoli
Home fries (potatoes and onions)

And, as others have said, they'll save for several months. The trick is not to store your onions next to other veggies, especially not next to potatoes, and in a cool, dry place. They'll last at least a month and sometimes longer.

One onion a week? We eat 1 onion for dinner almost every night! Yup, we are about 7 onions a week and there's only 2 in our household. I can't imagine rationing out 1 onion to last a week...

Kay from the Netherlands has a great recipe for stuffed onions:

http://thepioneerwoman.com/cooking/2009/01/stuffed-onions/

i freeze my onions straight out of the bag. cut the onions rings either in half or leave whole, pack them in a zip lock bag and place directly in the freezer. you can remove as few or as many frozen rings as you want for recipes and never worry about the rest going bad. they cook up exactly like fresh onions. i use them in steamed, mixed veggies, rice dishes and soups.

If you have a cool, dry, dark place to hang them, you can store them in a leg of pantyhose and they'll keep for up to six months:

via LifeHacker

How about an Onion Confit? The onions are carmelized with apricots (and cranberries if you like) and make a great side dish for pork or even on a plain hamburger patty. It will keep several weeks in the fridge. This weekend, I'm going to try putting up a batch in jars and doing a water bath process.

Here's the receipe I found on the internet. I usuallly leave out the cranberries, makes the confit look strange. Wish me luck with the canning.

Cranberry, Onion, and Apricot Confit

Yield: Makes about 3 1/2 cups

Ingredients

2 pounds onions, sliced thin
1/3 cup sugar
1/2 stick (1/4 cup) unsalted butter
2 teaspoons minced garlic
1/2 cup red-wine vinegar
1/4 cup water
2 cups cranberries, picked over
1/8 teaspoon salt
1/2 cup chopped dried apricots

Preparation
In a skillet cook the onions and the sugar in the butter over moderate heat, stirring, until the onions are pale golden, add the garlic, and cook the mixture, stirring, for 1 minute. Stir in the vinegar, the water, the cranberries, and the salt and cook the mixture, stirring, for 10 to 15 minutes, or until the berries have burst and are softened. Stir in the apricots and cook the confit for 1 minute. The confit keeps, covered and chilled, for 2 weeks. Serve the confit warm or at room temperature.

Note: the onions will give off a lot of liquid, just keep simmering until it evaporates.

Here's the original link. Enjoy!

http://www.epicurious.com/recipes/food/views/Cranberry-Onion-and-Apricot-Confit-13372

Gourmet | November 1991