Is it OK to use personal email ID for faculty job applications or should we use (current) institute's ID I am about a graduate from my university. Will it be OK to use my personal email if I am looking for faculty jobs/postdoc positions. Will it somehow give a negative impact on my application as compared to those who apply through any institution's link?
If you have an institutional email that will still be accessible for the foreseeable future, I would suggest using it. When I see applications for academic positions that use @hotmail.com or something, I sometimes (subconsciously perhaps) judge the application to be of lesser desirability.

However

This momentary judgement of the applicant's email address is quickly dismissed if the rest of the application is quality. If you are using a good @gmail.com email address or something similar, there is no shame in that. It should go without saying, but obviously do not apply for faculty positions with an email such as pick_butts@yahoo.com (or whatever). Even an email like sparkle.38@gmail.com should be avoided. 

I would suggest creating a nice gmail address specific for just your applications. 


  Roger.M.Turley@gmail.com (assuming one's name was actually Roger M. Turley)


This will allow you to be professional in your presentation as well as funnel all necessary correspondence to a specific and single purpose email account.