Can I evict this tenant?

[Tina Nguyen]

It is 4 am but I can't sleep. I've rented one of my properties to a section 8 tenant. It is a nice house in a nice neighborhood. I just spent about $6k to repair the house so I can say that this house is in very good shape. I accepted a section 8 applicant. After passing the inspection from the Housing, I let the tenant move in right away while waiting for the approved contract from the Housing. Big mistake! After two months living in my house, this tenant keeps calling me days, nights, weekends to ask me to clean some trash in the garage, in the back yard that left from my contractors, to show her how to reset the heater, to check why the oven is not as hot as she wants. She is really pissed me off yesterday when I received a message from the Housing stated that it was an emergency request to fix my A/C within 25 hours. I am at the stage that I just want to kick her out to not have to deal with her anymore.

I've received the lease contract from the Housing but I am still waiting for this tenant to sign the contract. She paid me her rent of $200 per month. The housing supposes to pay me the remainder of the rent. I haven't received any payments from the Housing yet because the tenant hasn't given me back the signed contract that need to be submitted to the Housing.

So, can I ask her to move out immediately since there is no contract yet and I haven't received the full rent payment? Do i have to serve an eviction letter?
I really appreciate any feedbacks. Thanks.