Hello sir..

Since you have asked about ISRO, I am assuming you are an Indian national(a mandatory criteria for a job at ISRO). ISRO conducts yearly examinations for the post of Scientists/Engineer in the Electronics,Mechanical and Computer Science domain. Check out this page for notifications- Careers - ISRO . The application deadline for 2016 recruitment(May 25,2016) just passed by.

ISRO also provides you with past years’ question papers for preparation. Check them out over here : CENTRALISED RECRUITMENT TO THE POST OF SCIENTIST/ENGINEER 'SC' IN THE DISCIPLINES OF ELECTRONICS, MECHANICAL AND COMPUTER SCIENCE

As for NASA , here also, there is a citizenship mandate(you have to be a U.S. citizen). However, this can be waived off for exceptionally valuable candidates. Check out the pages(10–13) from the below link in succession. It guides you through the educational and professional requirements you need to possess to be a successful hire - NASAJobs

A mechanical engineering degree is highly beneficial if you want to get into Space Technology. So, All the best ! :)