I suspect my mail id is being opened and read by someone who has come to know my password.
Is it possible to know the person who is using my ID?
And is it possible to open same ID on different computers simultaneosly without having an idea that it is opened on some other computer also?

No its not possible to know who, so change your password immediately.

And yes, it is possible, depending on the type of e-mail account, to be logged in from different computers.

Use a strong password. Eight to ten characters to include numbers upper and lower case letters and nothing that is a word remember to throw in a couple of those things that appear above the number keys. If you use a week password you will be compromised especially on most online free mail services. What about your online banking. Use a different password for every site make them all strong passwords and change them often.