I have been living with my girlfriend for 18 months in my house, how do I get her out?

It doesn't appear as though she can sue you for any sort of support.  However, peacefully removing her from the premises may not be so easy.   For practical purposes it may be difficult for her to prove that she is a tenant.  The food purchase could be argued that she bought her own food and the cable bill in her name could be explained that when she stayed with you she liked to watch cable so she paid for cable.  She may possibly be considered a licensee (no tenancy rights), if you allowed her to stay.  What you have in you favor is the fact that she did not sign a lease with the landlord, she did not make any lease payments, she was merely a person you dated that happened to stay with you (licensee).   What if shoe was on other foot --say she decided to move out and not honor the rest of your lease agreement? You and/or landlord would have no sure recourse that would be worth it.  Or you decide to move out and leave her there, what recourse does landlord have against her? None ($), but could change locks or evict her.  Difficult and slipperly slope but I would go out on a limb here and say if you changed the locks and boxed her stuff she would have a very tough time proving her tenancy and would have to spend a lot of time and money chasing you and proving she was wronged.   If she filed suit, claiming she had an implied lease, a good counterclaim would be that if the court finds she was an implied tenant then she owes you 18 months back rent and once that is paid up she can have the place.  When it comes to real estate matters and particularly rental issues such as this, I usually advise clients to act swiftly.  In this case, if she calls the authorities, have the lease ready and show them so that they can see she is not a tenant.   This is one avenue, the other is to take the long conservative approach and treat her like a tenant and attempt to evict her  -- this will certainly cost you time and money.  

If she has been paying for utilities/food she may be considered to be a "tenant"; otherwise she will be considered to be a "licensee"; that is someone who entered and remained on the premises with permission. 

In either event, now that permission for her to reside with you has been revoked the lawful way to remove her from the premises is to serve her with a notice to quit (typically 30 days).  If she fails to leave at the end of that time you will have to go through the requisite procedures for eviction in your state.  Once the court enters an order for her to vacate the property it will be enforced by the sheriff, using physical force if necessary.

What you need to do now is to speak with an attorney in your area.  They will advise you on the correct procedures for all of this.  If you fail to comply with these procedures you could find yourself on the receiving end of a lawsuit for unlawful eviction.  Therefore, tempting though it may be, do not use any "self-help".  While you may be able to lock her out, return her things, and have this all over; if she decides to pursue a case against you, it could be far costlier than an eviction proceeding.

As for suing you for support, absent some sort of legally binding agreement, she has no rights against you in this regard.