I want to know any website designing company in India which provides all IT services like designing website pages , designing graphics , providing affordable search engine optimization (SEO services) and also data processing service preferably in West Delhi.

yes there are many companies in india , India is also doing good in It sector. companies like

http://www.expertitsolutions.biz
http://www.e2solutions.net
http://www.aford.net or afordinfo.com