If you are using the Windows live email client (not webmail) open Live mail client, select the email account and inbox, highlight all the emails in the selected account inbox, right click drag them to a empty folder on your desktop, when you release the right clcik you should get a context menu, select "copy here". this will copy all the emails to that folder in the .eml format, then you should be able to import them from that folder using this extension for Thunderbird (newer versions of Thunderbird may be able to import .eml format without the extension, not sure)
Note: When dragging to the desktop folder it may appear it is doing nothing, be patient it takes a while to convert them to .eml format, and depending on how many emails you drag how long it takes.
Do this for each email account and folder you have, label the folders you drag them to, this keeps them sorted for import purposes.
Importing the address book can be a little trickier