Php Login Class - Security and Logic check
Security


sha1 is not secure enough for password hashing as it's way too fast. This is also noted in the documentation. Use bcrypt instead. 
=== is not timing safe, use a timing safe string compare instead (bcrypt does this for you).
You should really use salts when hashing passwords (bcrypt does this for you).
You shouldn't safe the password in the session data.


Misc


Your formatting is all messed up, leading to less readable code. Your indentation is off quite often, your usage of newlines and curly brackets is inconsistent, and you should really always use curly brackets, even for one-line statements (to reduce bugs and increase readability; return false; return false; eg is hard to understand, especially with your indentation).
if (cond) return true; else return false; can be written as return cond.
Binding the session to the ip increases security, but decreases usability (eg for mobile users). 
Having three nested ifs instead of one if with &amp; can sometimes reduce readability. 
You seem to use == and === interchangeably. In most cases, === would be the correct choice, as it can avoid bugs.
You should only create one db object and pass that around, instead of creating a new one each time.
I'm not sure what verifySessionUser is actually used for. The user didn't set the user id, you did. So it should always be correct, and the check should be unnecessary.
getSession: From the name, I would expect that this returns a session. But it doesn't. isLogedIn seems more fitting. And then I would rename verifyUser to logIn to make it fit.