As of last night, my room mate gave me notice that she wanted me to move out by the 1st of October. Which gives me a window of 7 days. She then said that she didn't have to give me a 30 day notice merely because my name isn't on the 6 month lease of our apartment and her dad is. Is it not true that a 30 day notice is to be given?

First tell us what state this is in - it's important as laws vary. You are considered to be an "at will" tenant (no signed lease) and the landlord can ask you to leave with either 15 or 30 days written notice (depending on the state). If you aren't out by that time then the landlord can start the formal eviction process.