Pictures of the area in question may help.

OK, here's a rough shot...

Here is an idea for a patio. I built this one across the back of my house and I am growing fuzzy kiwis on the pergola.

That's very nice...not sure how I would adapt that for the skinny space with a swale that I am stuck with.

Where do you live? (city and state) because plant and paving recommendations vary by location. And where is the swale?

That area has a lot of promise if you give up on the grass.

1 - make a series of shallow retaining wall terraces up the slope to stabilize it.

They can be made of recycled materials like this one:
http://www.pinterest.com/pin/210754457534502904/

2 - Plant the new terraces with easy-care perennials that can thrive in that location

3 - Do some landscaping with shade-tolerant shrubbery to sort of hide the corners of the house to make the area look larger, then lay out your sitting area. Just think of a small place to sit in the cool shade and have lunch or tea.

http://www.pinterest.com/pin/210754457533417326/
http://www.pinterest.com/pin/210754457533637731/
http://www.pinterest.com/pin/210754457533416622/

Those are all great idea--I like the last picture the best. How are those stones set into the ground? Mortar? Or just on top of a gravel base?

I live in Virginia, and the "soil" is mainly clay. The swale is visible in the picture--look at the small leaf pile and follow it straight out (see how the grass doesn't grow, and we've lost the topsoil?)

Hi, I am a garden designer and wanted to say your spot is not impossible at all! It has many wonderful possibilities, in fact, but you are right that trying to keep it planted with grass is not one of them.

You should definitely replace your grassy slope with drought tolerant plants; more plants would also help prevent the erosion you are having. It doesn't look like shade is as much of a problem for the grass here as the dry conditions and eroded top soil. Look up lists of drought tolerant plants as there will be very sharp drainage there. Some low shrubs towards the top of the slope and then perennials lower down would look nice.

lazygardens has given you some great inexpensive paving options. The last one that you liked might be hard to get a contractor to build as it takes some creativity. It looks to be set in sand, but could be done either way (cheaper in sand, plus better drainage).

A low retaining wall will keep dirt and mulch from washing onto your patio area. To follow the third pinterest idea sketch out an irregularly shaped area behind the house, leaving generous space (at least 4 feet) close to the house for planting beds. Here you would have all shade plants (hostas, carex, ferns, heuchera, geranium, tirella, bleeding hearts are a few).

On the uphill side of the patio, your retaining wall could be a serpentine wall of stacked stone. It doesn't need to be high, less than a foot even, to hold back runoff from the slope. If it is not cemented and not too high, you can keep your cost down. You could even build it yourself. There are usually quarries that will sell you bulk stone (I used to go to one in Falls Church, VA that would weigh my car before and after I filled it and charge me a per pound charge.) Be sure to build in a bit of gravel on the uphill side of the wall to prevent water build up over time.

Then I would draw up a planting plan for your hillside. Assuming it is south facing (since the side of your house you said is north facing), you will want tough sun-loving, drought resistant plants.

Here are some that I like that should work in Virginia:
rosemary
thyme
bear berry
day lilies
juniper
santolina
lavender
heather
sedum (many varieties available).

The list of options if very long. If the slope is really shady, as you suggest (though it doesn't look shady?) then your list of options for dry shade is shorter, but still there are some tough plants out there. Google "plants for dry shade" and you should find lots of options.

You will want to mulch well to start and probably bring in compost to put in with each planting since your top soil is so badly eroded.

You could post your planting questions in the perennial forum and you'd get tons of help there.

A garden designer in your area could assess your location and draw up a plan for patio and planting for you. I hope this helps. I think you could have a lovely bit of paradise back there with a little work.