Here is one more image

1. Remove the existing grass and till the yard
Never till in preparation for a lawn. When you rototill the bottom of the tiller digs to different depths. When you level the top, that will give you different depths of fluffy soil. When that soil settles, it will settle to the profile of the non-level layer of untilled soil underneath. But yes, remove the current grass. Best way to do that is with several applications of roundUp at 1-week intervals. Water heavily in between to get as many weeds sprouted as possible.

2. spread nice quality top soil/compost mix
Nope. Your current soil is the best soil there is. All you have to do to fix it is feed it with the alfalfa. Unless you have drainage issues you wish to fix, then adding or removing top soil should be forbidden.

3. apply alfalfa fertilizer
Great idea.

4. Install st augustine sod.
For the shady area in the picture, St Aug would be good. Can you get a mower in there?

St Aug is mowed at the mower's highest setting. Bermuda (your back lawn???) is mowed at your mower's lowest setting. Don't get those two mixed up.

The reason you have weeds is your turf is not dense enough to keep the weeds out. Bermuda in the shade will never be dense enough to keep weeds out. St Aug needs to be mowed very high to keep weeds out. Second reason (maybe) you have weeds is watering too frequently. The soil should dry out completely at the surface before watering again. In the winter that means once a month max. In the summer that might mean as much as once every 7 days unless you are having an unusual drought coupled with dry winds and weak/sandy soil with pounding sunlight (like Las Vegas). If your grass will not go that length of time without water, then you are not watering long enough when you do water.

Thank you dchall for the response.
1. Okay no tilling :), by removing the grass i meant digging up the existing grass and weeds completely until all i see is only the soil. or should i still do the round-up method.
2. The reason to add more soil is because i might loose some when i dig up. If that's still a bad idea then i will avoid adding top soil. As i am a total novice to this, can you please give more details on why we should not add top soil/compost

As far as watering, i am following whatever is said in the Organic FAQ, may be i need to check my sprinklers and do the 'can' test

One last thing, is this the right time to do all these or wait until april?
Thanks again for your inputs.

1. Now that I see this in writing I realize I gave a fairly specific suggestion to use Round Up in the organic forum. Please accept my apologies. If you would like more information about applying chemicals, please check the regular lawn care forum. Just digging will not remove bermuda.

2. I'm not sure how you lose soil. Can't you just sweep it up and put it back? If you add topsoil you will change the drainage. If you have a low area, then you might want to add topsoil to avoid standing water. Looks like your situation is a hill, so I wouldn't see a need for topsoil. Compost is a different subject. In my opinion, if have all the soil microbes, you probably don't need compost.