Your over-tenant, the person you rent from, should only enter your room by giving you prior notice and with your consent. Since you are paying her rent and there is no lease with a clause describing when access should be provided, you have an exclusive right to possession of your room. As Mr. Weinman explained, the tenant may have already taken steps to terminate your tenancy and you may end up in court after July 1. Under no circumstances, however, does the tenant have a right to evict you without first taking you to court.
The above constitutes general information only and should not be considered legal advice.
Putting aside whether the sublet is legal or even permitted under your landlord (the tenant's) lease, she should terminate your month to month tenancy with a 30 day notice, which may have been properly served in May giving you until June 30, 2014. Was it a written notice and if so, how was it served upon you? If it was properly served, on July 1, she can make a petition to commence the eviction. At that point, the courts will be involved.
I'm just 3 "helpful" answers away from a free toaster-oven! I may be guessing or not licensed in your state. No atty/client relationship exists.