DO NOT TILL, just to follow up and agree with neliaz. If the contractors left your soil surface uneven, then the box blade is the universal solution. If you sod, you can do that any time from now on. If you decide to go with seed, wait until mid June. Bermuda seed needs hot soil (not hot air) to germinate. That would give you many more months to worry about erosion. Until then you can just mow the weeds and practice taking care of it like it was Buckingham Palace. Seeded bermuda and sodded bermuda are two different varieties of plant. They do not mix well in a yard, so think about that before you go buy any seed. Never seed bermuda to patch up a thin spot of hybrid (sod) bermuda.

The boxscrape is otherwise known as a box blade. It is used by landscapers and finish graders to put proper drainage into a project and to properly prepare the soil for seed or sod. When this tool is on a tractor, an experienced operator can tune up a yard like yours in less than an hour; however, put it on a bobcat or skid steer and they will take a week to do the same job. Here is a picture of it in action. From the vantage point of your picture it looks like the whole neighborhood has no drainage. Looks like one yard drains onto the next yard instead of out to the street. That might not be the case, but you have to watch for that in the neighborhoods which are essentially level. If you check around and find you cannot afford a landscaper with a box blade, then this becomes a DIY job. Search this forum for topics about leveling a yard with sand. Basically you bring in more than enough sand in bags (you can return unused bags), spread the sand, level it, water it to settle, spread more sand where it sunk, water, level, spread, water, level, spread until you are happy. The important thing for you is to get grass growing and stop the erosion. Where has the soil gone that you brought in? And are you serious that you have 2 feet against the house? Can you post a picture of your current worst spot? I used to be work for a finish grading business and might be able to help you fix it without over fixing it. NOW IS THE TIME FOR THIS PROJECT. If you wait any longer you will not get your grass seed in before winter. In fact it might be too late, but I would go for it. Spray the weeds with RoundUp, level quickly, scatter seed, water 3x per day for 3 full weeks or until you get 80% germination of the new grass. Don't worry about weeds yet - just get the seed down asap. Get a full sun seed mix from the local hardware store. I say that knowing that it is not the world's best seed, but it is what you can get NOW without researching the fine details of the best seed for your area. Read the Guaranteed Analysis on the grass bags. Look for one that has no rye grass in it. Fescue is okay (not great), but definitely no rye. That is unless you had your heart set on a full rye lawn. The main grass should be varieties of Kentucky Bluegrass, possibly with some tall fescue in it. Spread at the rate recommended on the bag. Don't worry about spots that do not come in as dense as you expected, because KBG will spread to fill those in next year.

I'm sure that you can get a lot of helpful advise if you post this on the Organic Lawn Care Forum. They will tell you how to work with your soil to level and enrich it before seeding your lawn. Tell them where you are located in Kansas and what type of soil you have (sounds like heavy clay). I have learned a lot from them - they're the experts. Their FAQ is helpful too.

Do you have cloudy days to take pictures? The contrast is too high to get a good look at your grass. I'm getting a feeling that it's nutgrass. Nutgrass is not a grass. It is a sedge and must be killed with a sedge killer. Nutgrass is also a swamp type plant that thrives in soggy soil. Stop watering until about April and then water once, deeply, per month until the temps get into the 70s. Then go to once every 3 weeks. When the temps get into the 80s go to once every 2 weeks. Keeping the soil dry like that will severely discourage the nutgrass without hurting the turf.