first of all let me tell you that i have a similar problem to you! although my scalp does not peel or itch, it has this strange smell you describe even hours after i have washed. if i don't wash on one day, it smells terrible, this sebum like smell and then i shed a lot of hair.
but there are things you can do to help it or even make it do away.
one of the things that helped me the most is a detox i did using Arise and Shine products and following the dr. richard anderson cure! its absolutely mind blowing. almost all your ailments will disappear within two week of starting the cure. but the secret is to take lots of flora grow ( a probiotic formula) while your one the cleanse. this will rebalance your intestinal flora and rid you of any candida or similar fungus which then has an incredible effect on the scalp. BUT, the cure does not last for ever and conditions do return after a while when sluggish eating habits and other old waste is methabolised. hence i suggest repeating the cleanse a couple of time, like 2x year at first and then maybe once a year or so or until all your health conditions are restored.
the other quick fix, for your scalp is the following
grind and soak one table spoon of fenugreek ( methi) seeds in 250-350 ml very hot water (ie pour boiling water in the mug or container in which the ground seeds have been placed). let soak for several hours or overnight.
after you wash your hair just poor the strained cool stew over your head/scalp and use some to message. it give your head a pleasant smell, beats hair loss and is highly effective against all types of itchiness/flakiness etc
if you are very keen what i would suggest doing is, applying a few drops of neem oil to your scalp before bed time. message it in and leave overnight.
In the morning shampoo your hair and then do the fenugreek rinse!
this works miracales! your scalp will be fixed in less than 48 hours
However, you have to understand that the hairloss can be imporved with external remedies but not cured! yoiu will need to undertake an internal progamme to over come yoiur hairloss for good.
Also Propecia, although a normal prescriiption drug, is highly effective for hairloss and if you take it along with the cleanse your get hair like you have only had in your dreams.
anyway these are a few tips. i have literally tried everything on the face of this planet so trust me on what works!
there are couple of other things that can be done, but try these ones first and if you are not satisfied you can get back to me