Dealing with sketchy people

I've been running this 501st blog for a couple months now, mainly reporting articles and pictures and things, as well as things I do with my armor and events.
Over this past weekend, on a troop, I was approached by a number of... well, sketchy people. A couple were the regular homeless on Church street, another was an odd woman ("Are you a space man? Are you going to space?", then about face, walked away) and a woman who was high off of her mind.
The first three weren't bad, but the last one wouldn't go away for a couple minutes (she kept poking me in the chest, asking nonsensical questions and singing, loudly and badly) - it's not exactly the type of attention I want, especially when there are kids around.

What are some encounters that you have had while out in public?

The reason I bring this up is I'm planning on doing a write up based on some of my personal experiences for reference - how do you deal with people like this? How do you protect yourself?

I had a wrangler for both days out in public, and in other public events, but at times, even they are at their limits.