My project will be completed this month end and therefore my work Visa will be cancelled by my employer though it is valid till next year.
My questions are

1) How long is one allowed to legally stay in Germany after Work visa cancellation. Does one have to leave very next day.??

2) If there is any other temporary visa one can apply for if I want to stay for a 1-2 months after project completion.

pls advise.

Since you have not given any proper background details the answer is

1. Yes, leave the country next day
2. No

But if you can give some more information then it may be possible to give some advice
1. how long are u in germany and under which visa?
2. What kind of work-contract did u have with the company?