Well, you said it all, basically. Facts are thus:
1.) You don’t have a written agreement, which means you have a “common law” agreement. Since you pay week-to-week, this means you’ve established a week-to-week common law lease.
2.) The owner has made the situation hostile, forcing you to terminate when you otherwise wouldn’t. One could argue that their behaviors were intentional acts, intended to drive you out early.

Can they do it to you? Sure. You can do anything to anyone and get away with it if the person you’re doing it to doesn’t do anything about it. Do they have any grounds to pursue you for the last month of rent? I highly doubt it. That doesn’t mean they won’t try, just that I personally don’t think they’re going to get very far at all if they do. It wouldn’t be worth their time to bother. If I were you, I’d stop communicating with them, find a new place to rent, and forget they exist. If you get served with a summons you can seek legal advice then, but their complaint will likely be a small claims issue that won’t be taken seriously by any judge, since their claim to the 30 days of rent money isn’t worth the paper it (isn’t) written on.

I’m a booth renter that has just been given a notice that my lease will be terminated after 30 days. All because I had a difference of opinion….then a week later when the owners wanted to discuss it a half hour before scheduled clients, which I didn’t agree with and said no let’s try for another time, they got upset and two days later I had a notice in my drawer because clearly I was unhappy there??? Well we don’t have a written lease agreement….we basically pay rent week to week there not month to month, but they are telling me since I left 3 weeks early ( because the owner was passively aggressively harassing me in the back room) I owe for the remainder of the month due to our month to month agreement. I’ve left once before and gave them a 2 week notice that was cut short because the owner was yelling at me in a stairwell and I didn’t feel comfortable staying. I feel that I am being bullied and I don’t know my rights. Can they do this to me?