No you can't just be kicked out with no notice. If you're subletting ilegally because your lessor has no right to sub-lease to you (or if she needs to get their consent, or if the apartment requires you to sign a lease with them), then you can be evicted. If you're late paying your rent, you can be evicted, even with an oral sub-lease.
Eviction is a multi-stage process. 1st you need to to be given notice. If the basis of the eviction is non-payment of rent, you get 3 days notice to "pay or quit." If you're not late paying rent but your tenancy is month-to-month, as yours is, you can be given 30 days notice to leave. Then if you don't leave by the deadline, you have to be sued for Unlawful Detaine. UD lawsuits can take weeks, if you don't defend, or months, if you do defend.
Being sued will damage your credit, so you may want to get out of what has to be an uncomfortable living arrangement ASAP.
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