If my female friend has been living with me for about 6 years now and she has basically turned my home into a storage unit, how do I get her out?

At this point in time even though there is no rental agreement (either written or oral) and since she has paid rent, your friend has attained the status of a "tenant". Consequently, you will need to serve her with notice to vacate (typically 30 or 60 days). If she fails to leave by the date specified in the notice then you will need to go to court and file for an "unlawful detainer" (i.e. an eviction lawsuit). In the meantime, don't take any self help measures such as locking her out, removing her personal belongings, etc. You could be sued for unlawful eviction or worse if you do. Once a judge issues a writ of possession (or your state's equivalent), you can then have a sheriff remove her if necessary.

At this point you may want to consult with an attorney in your area who specializes in landlord-tenant matters or at least contact a tenant's rights group for further information.