@Jade Wong I've actually never had to evict a Section 8 tenant in California (only NY state), but I'm usually working on the opposite side of the coin here in California, with the low income tenants, so I've seen my fair share.
Oakland's PHA (along with SF and other big cities) has a fairly strict and regimented set of rules for things like evictions, rent increases, etc that smaller area PHAs are usually much more flexible about. I'm not well versed in Oakland housing rules, with my experience being primarily the North Coast counties, SF and the counties south into the Central Coast. I know generally in California, the length of time you must give a tenant notice (30 or 60 days) to end a month to month agreement is based on the amount of time they have been in residence there (more or less than 1 year). Many California PHAs use those same rules for the notice they require. I'm not very familiar with SD, perhaps their PHA uses a minimum 90 day notice, but that is not the case everywhere.
My personal opinion is that it sounds like they've been in residence long enough where they would be granted a 60 day notice period, so I would give them one pronto. You can also probably start the eviction process based on not allowing access to the apartment for repairs with appropriate notice (which I'm assuming is stipulated in your rental agreement) at the same time, if they're going to give you more trouble.
Since you're uncomfortable with the current tenant situation, and the situation is more complex than just a normal tenant not paying rent, its probably worth your money and time to hire a professional service/lawyer to help with this eviction. If you follow what they do closely, you can likely use it as a learning experience and perhaps be able to do them yourself in the future, need be.
Please let us know how it goes!