iPhone sending a lot of packets addressed to weird destinations, draining battery quickly
You jailbroke (is that a word? jailbreaked?) it, thereby opening the door to any application doing anything with your hardware. And now it appears that some application is doing something with your hardware. Your phone is compromised and is now trying to compromise other devices on its netblock. You're carrying a virus infection vector in your pocket. 

I recommend a full restore absolutely ASAP, and I recommend really thinking about whether jailbreaking is for you.

I'm not anti-jailbreak. I just think people aren't aware of the full repercussions when they do it. Apple's not just being arbitrary in only allowing vetted software onto the devices. It's not JUST a business move on their part. It also protects users from exactly what has happened to you.