You're not going to fix that in two weeks or less. May as well begin by adjusting expectations.

For planting areas -- cover with several layers of newspaper and then a couple of inches of mulch of some kind.

For lawn -- you don't indicate what zone you're in or otherwise what the cultural conditions are (smount of sun, soil type etc.) If you're far enough north, you can still do some overseeding with grass seed. Wherever you are, raise the mower blade to the highest level. Mowing high is the best way to give the grass a chance to overtake the weeds.

There are two lawn forums at GardenWeb. I think you would get better suggestions from people who have been thinking more specifically along those lines. But before you leave this forum, check the FAQ pages. Near the bottom is the Organic Lawn Care FAQ.

When you post again, please note where you live. It is the single most important part of your question. The location determines your grass type options and often care options. For example, it really is too late to seed. Seeding is best done at the end of summer. Spring is a bad time to try it and late spring is almost as bad as mid summer. If you seed now you will have a crabgrass lawn. Just plan to wait until the end of summer. You'll be less frustrated and have much better results. For now I would take the best care of it I could. Not all grasses like to be mowed high. Some will practically choke themselves out by being too tall. But even a weedy yard that is watered, mowed, and fertilized properly will look pretty darned good. Simple mowing is enough to keep many weeds away.

Check out the FAQ here and those other forums.

Torching sounds like a great idea. Get a weed dragon, fry it all and lose the lawn altogether. No mowing allergies and you can smother the weeds as Mary suggested with paper or cardboard and design a yard with crops, perennials, shrubs and trees instead. Sounds like you'll have to rebuild the soils or make raised beds, but it can all be done organically.

If the yard was that badly neglected the soil was also so the best place for you to start is with a good, reliable soil test so you know where the soil pH is as well as the nutrient levels so those can be properly corrected and you can start with a good healthy soil.
Rototilling, and adding organic matter at that time, may well be you best option right now.

Start a compost pile!

For the flower beds and vegetable areas: Use a string trimmer to shorten the weeds. A couple of layers of cardboard to kill the weeds, mulch thickly with tree shreddings (call local tree maintenance companies and ask if they can dump wood chips on you) and plant through the cardboard.

For the lawn area: mow it short and keep it mowed so the weeds can't set seed. Close-cut green weeds aren't too bad. Figure out what to do later. Fall is the best time to redo lawns in most of the US, so you have time.

Mowing grass short does not help create a good healthy turf because the shorter the grass blades the less material available to utilize sunlight to manufacture nutrients that will help the grass grow, and grass cut short allows the sun to reach the soil where the "weed" seeds are which will encourage them to germinate and grow. Cutting your grass high will put more grass blade out there to soak up sunlight and manufacture nutrients htat will feed the plants which will encouarge them to send out more leaf, and on and on, and the taller grass blades will shade the soil and help keep "weed" seeds from germinating.

Right. Worst thing you can do for a weedy lawn is scalp it. Mow high, mow high, mow high.

Kimmasr and marymd - The objective is not to create any sort of a lawn. It's to keep the existing weeds from going to seed and make it look a bit better while the OP is figuring out what to do.

Again, mow high. You'll cut off the seed heads, deny the existing seeds the chance to sprout, and you'll be giving what grass is there (or any newly seeded grass) a chance to grow. Really. Scalping will make the weeds worse.

Thanks for all the input everyone! I've started putting down some cardboard & newspaper like many of you have suggested & I'm guessing from what I've read here that the only way to correct the beds is with cardboard & good old fashion weed pulling. As for the lawn I just really want to keep the weeds from seeding to my flower beds once I clean them up so I guess I'll just plan on mowing high & do some reseeding this fall. Thanks again for all the info.

Mulching is the most crucial, most exciting, and most rewarding thing I do in the garden. (If you're going to mulch, make it a nourishing one or you'll deprive yourself of the joy.)

I used to use corn gluten meal on my lawn as a preemergent herbicide and I had good luck with it, it's also a nitrogen fertilizer. I over-applied it because my spreader didn't work so well, a 50lb bag for about 1500 sq. ft. The recommended rate is 20lbs/1000 sq ft. It used to be about $15 a bag and I bought it at a cattle feed store until they stopped carrying it. I wonder if they were tired of that lady who came in to buy one bag of feed every few months;). (I moved recently and haven't looked for it here in my new town yet.)

Since it's a pre-emergent, if you have to seed your lawn, do that first. If it's a creeping lawn like bermuda, you shouldn't need to seed it. But it doesn't transform your lawn in two weeks, and it doesn't do anything to weeds that are already growing. For perennial weeds like dandelion, you either have to pull them or just wait for them to die of old age, but at least they won't reseed and spread. Also you have to time the applications to before most weeds sprout, of course--late winter before the henbit and chickweed sprout, then spring, then late summer. Depends on what type of weeds you have and your climate zone and all that.

The abundance of weeds most likely means the previous owners didn't use herbicides. That's good. "Neglect" can have it's benefits. Cut early before flowering, those weed clipping can be a nutritious mulch. A weed free, too green lawn would be a far more disastrous scenario for me.