Hey aditiagr --

We're not too familiar with the phrase "at short notice" - this isn't something we remember hearing before. It doesn't sound incorrect however. If it were to be used, we'd think it would be equivalent to "on short notice" which is the more common usage.

The phrase "on short notice" simply means that there is little advance warning. "He had to prepare for the inspection on short notice when he was told that his manager was due to arrive in an hour."

In the other two examples you've listed, the proper use is to put yourself last in the series. This is true regardless of how many others are being named. In both of those, it would be better to say "You, Vaibhav and I will get an award" or "You, Vaibhav and I must take the blame" -- so the speaker names himself ("I") last. (And, you'd also say "You and I will get an award" if it were just two being named.) Similarly, you'd want to name "you" (the person you're addressing) first in the series.

Hope this helps!
EssaySnark

What I have learnt,read and used uptil now is 'XXX,you and I' (third person,second person,first person) irrespective of the tone of the sentence. I wished to know if this was correct.

I'm not sure if 'on short notice' and 'at short notice' are the same thing but I can't define the distinction.