I am looking for a 2 week-1 month situation. The reason making that limited stay is somply money.
I looked at Global Volunteers they seemed to have something in Warsaw every month, but the rate to register and stay with them for 2 weeks was 2600USD. :/
That's absolutely ridiculous, and I strongly, strongly suggest that you shouldn't pay such money. 2600USD is about 7500PLN - and for that kind of money, there's no reason why you shouldn't be able to come here for longer (you'll have 90 days visa free). The flights to Europe can be had for as little as 500USD return at the moment, especially from New York (I've seen 300USD!). That would leave you with around 6000PLN, which is more than enough to live here for 6-8 weeks comfortably, including living as a tourist.
I speak a limited Polish- but am learning more day by day with a class. I wonder if that would be enough to volunteer to teach English?
It should be more than enough - in fact, I'd be willing to bet that you wouldn't need any Polish whatsoever.
When you say I dont need someone to organize it for me, do you know of any local places in Warsaw that do that sort of stuff I could contact? I found something called the warsaw Insider online that has several listings of activities, contacted them but no response thus far.
What I'd suggest is just coming over and looking once you're on the ground. There's enough good people around that can help when you're actually in Warsaw - and even turning up on the doorstep and asking if you can volunteer should get you positive results. There's plenty of 'angielski dla dzieci' schools about - and I'm positive that 99% of them would love to have a native person helping them out for a few weeks.
Unfortunately, Polish people are notorious for not replying to e-mails. I think it's exceptionally rude of them, but it's the way it is. Face to face often yields much better results :)
Especially in Warsaw, you should have no problem at all :)