It's most likely a virus.
It could be done in two ways...
1: Somehow your wife's password was captured. The spam is sent from a remote computer which logged in with you wife's account. This may be because she signed in with her Messenger account on a phishing site. In that case all that's really required to stop it is changing your (your wife's) password, the answer to the secret question, and alternative e-mail address. When they have your password the have full control over your account, so they could have changed the secret question and such as a backdoor to get control back when you change the password. You can change all that through
https://account.live.com/. If you use the same password for other accounts it's also advised to change those passwords too.
2: The other possibility is there is a virus installed on your wife's computer which locks in to Messenger. When your wife is online the spam messages are sent without her seeing it. Do a virusscan with a good up-to-date virusscanner and a spyware scanner. If something is found you could try to let the protection software remove it, or remove it manually. But once a virus gets in your system there is no way of being 100% sure it is removed completely. It's usually simpler to backup your documents and restore the OS using the system restore CDs that came with the PC, or do a fresh installation of Windows. Remember to fully update windows after a fresh installation or system restore.
Not everybody will agree with removing the OS after a virus infection. I might sound paranoid, but I gave up on trying to remove a virus and hoping there's nothing left hiding somewhere in the system. Especially on machines where there aren't that much apps installed anyway and re-installing everything won't take days.
So to be short: At a minimum do a virus scan, and change the password, the answer to the secret question, and make sure the alternative e-mail address belongs to you.
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