Weeds are simply any plant that is growing where you don't want it to. Some say it is a sign of unhealthy soil. Actually, the more diverse your weeds are, the more healthy your soil is. Think about it. If the soil of an area is that bad, then it would be bad enough to not even support weeds.
The following pdf is a more thorough explaination of
Soil Solarization
There is no quick, organic method by which to get rid of quack grass, crab grass, bermuda grass. The problem with tilling is that it just breaks up the grass into little pieces and gets the nodes more thoroughly distributed in the soil. So long as the node is alive, it will develop into another plant. In many ways this intensifies the problem.
I don't know how large your area is, but here is what I did when I built my beds. This may not be the best method for everyone. I covered the areas of lawn that I wanted to turn into beds with thick layers of cardboard and newspaper or roof shingles or really thick layers of leaves to block out light completely. After a couple of weeks, the unwanted grass that was growing in the area is significantly weakened. I'll wait until we have a major rain so that the ground is soaked, then wait for it to dry enough so that the soil is loose and crumbly, never work it when it is muddy or you'll ruin the soil structure. It is incredibly easy to sink a spade in the soil while in this state. If you don't want to hand sift, a pitch fork also works well.
I'll use my spade to go foot by foot, turn the soil and hand sift out the stems of grass. Since the tops have been devoid of light, they can't feed the roots which significantly weaken. Enough so that if you lift a big chunk of soil you can quite literally grab a hold of a thick area of the stem and pull the entire length of the stem and the rest of the plant out quite easily. I like to hand sift the soil because once I remove the unwanted weeds and sift, I know I've gone thru every inch of soil and I never walk on that area again. I'll also take this time to incorporate compost as well. The whole process does take time but goes quicker than you'd imagine if you follow the procedure. If you get that much rain, raise your beds by simply mounding the soil in rows. Again, once you do this, you shoudn't have to do it again. Don't make them more than four feet wide so that you can reach in from either side. Raised beds will allow the soil to dry better instead of remaining wet.
It is best to do this in the fall so your soil can recreate optimum soil structure over the winter, but you can do it in the spring as well.
If you still want to go the soil solarization route, I'd do it asap since this is the time of year when most of us get our warmest temps. There is no need to do it "all winter".
With either methods, you may still have a handful of unwanted weedes sprouting. Take care of them asap when you can pull the quickly with two fingers or skim with a hoe instead of having to dig out a large mass later. If you an afford the time after either method, wait a couple of weeks to allow any weed seeds to emerge. Turning soil will always bring up dormant seeds to the proper level and environment to sprout. Take care of them and then mulch with a good two inches of whatever mulch you want to use. If for a vegetable garden, do not use wood chip mulch unless it's the only mulch you have access to.
With your soil properly prepared and mulched, you should be relatively weed weed free for the rest of the season. And with regular maintenance, you'll be ahead of the weeds.
Green manures are best explained here:
Overview of Cover Crops and Green Manures
Diatomaceous Earth will only help in controlling Squash Bugs when they are in their adult stage. It will not have an effect on eggs which can exist in the soil for months, the larvae, or the pupa. There is also no way to treat once and expect them to be gone even with chemical methods. If is is that much of a problem, consider not growing those crops. You can try to look for varieties that are resistant, but SVBs are persistent and you need to learn about thier life cycles and habits so you know what to look for, when, and how to control them at those stages (they'll never be eradicated).
Look here for more information on
Squash Vine Borers.
As for your cucumbers, you probably have the Spotted Cucumber Beetle or more likely and more destructive the Striped Cucumber Beetle. Learn more
here .But the only way to know is to inspect the damaged plant and see if you can find and positively identify the culprit before attempting control methods.
Solarizing? 
But, yes, I used black plastic on my beds to kill some sort of infestation (don't remember what kind it was, probably fungal) and keep down weeds. Something really did a job on my tomato plants several years ago, so I ripped them out early (like this time of year) and covered the affected area with black plastic until the following spring. It worked great. And there's one area just between one of our beds and the wall of the house where weeds keep popping up, so I keep that part covered all the time to protect the plants growing in the front part of the bed. Cheap and easy.
