Essentially, without a written agreement, there's no lease. I'm not a lawyer, so this isn't legal advice. But without a lease, at best what the tenant has is a month-to-month arrangement with you.
And I use the word "tenant" with some reservation.
Check with a lawyer, but my first reaction is that you've got two choices:
(1) Since the person wants to stay, if you're willing to accept fair market payments from him, send him a lease that requires monthly payments (not barter services). If he signs it, great. You now have a lease, receiving the payments you want.
(2) If you simply want him out, sent him a notice asking him to move within 30 days. And this is why I'm not a lawyer: I wouldn't even refer to him as a "tenant." That might establish him as a tenant, in which case you might have to go through a formal eviction process. If he's not a tenant, then there's no tenant to evict--simply someone who you've allowed to stay in the house without any sort of written agreement.
Check with a lawyer for more information.
Hope that helps.