Among Digital, Print, Radio, OOH, Television, Celebrity Branding etc which is the cheapest medium of advertising and why

Digital I guess, as Digital methods are cost effective because they are usually targeted for certain target market and does not cost too much comparing with other methods.

It totally depends on your STP, ya sometimes digital are cost effective but not always, celebrity branding is a different thing.

There is no straight answer to your question. There are various factors and dynamics that are involved before one decides to spend on any of these media. I mean, you can easily say that digital is the cheapest, but come to think of it, is it really cheap? If you are trying to sell a highly talked about product like say a Smarrt phone, then Google is gonna charge you a bomb for each of the related keywords. And it's a product that has almost universal appeal, then how do you pin point your TA so that you dont spend a lot? In such cases, a print ad or even a tv spot also may seem logical. But for a product with limited audience and unique usage, digital may be the only way.

So as I was saying, each of the media you mentioned and many more can be economical depending on what you are trying to sell (product) and to whom (positioning). 

hope I was of some help

Talking about lowest price advertising must bring "Viral" and "Guerrilla" Marketing, which has the lowest price and the highest impact on the market, not easy to come up with creative concepts for the same, but I believe those are the coming era, I had a TV interview 2 years ago talking about Guerrilla Marketing, might give you a good idea about the topic "In Arabic" http://www.youtube.com/watch?feature=player_detailpage&v=nJn4LZi-W_0#t=18s