I can definitely sympathize. Weird strangers just seem to love me for some reason. When the conversation is inherently short (ATM line, passing someone in the grocery store, etc) you can usually smile, say something neutral like "wow, sounds like its been a rough day" or "yeah, that is sort of bizarre," then quickly move on. If you're stuck somewhere, like the bus, I would say basically nod along unless you can't in good conscience (they're saying some offensive, etc), in which case a short "well, I can't say that I agree" should suffice. If they persist, you should be able to tell them that you're just exhausted from a long day, distracted by other things, whatever, and aren't in the mood to debate.

If you know it's going to come up on your commute, bring a book and/or earplugs. I had some bizarre people try to talk to me oftentimes when I would wait for the bus, and headphones tend to do the trick.

On the lighter side, I heard a comedian say that when a stranger got mad at him and started an awkward confrontation, he just started a completely different argument. As in "the light is green, go!" "well, you should give me my jacket back!" "what?" "I said you could borrow it, not have it!" Maybe you can just start a random conversation of your own, on a completely different topic :)

Just give that stranger a one word answer as much as possible... Don't look in the eye too while answering. This could make him feel as if you're not interested.

If this doesn't work, pretend as if you're doing something example you're reading, or using your phone just so he/she could stop from talking to you.

If you have a chance to escape, then do so.

If they seem like normal, friendly people I'd try to make a bit of polite conversation. I'm always just a bit uncomfortable with strangers anyway, and you never know, I might make a new friend. And it think that sometimes, strangers are angels unaware, you never know, why blow your chances? If the person seemed weird but unthreatening I'd probably stay to talk with them because sometimes those are the most interesting people. But if they were putting the make on me or I felt unsafe I'd find some convenient excuse to walk away.

http://farm1.static.flickr.com/74/181808569_715e3381c5.jpg

I am one who doesn't mind getting into conversations with strangers quite a bit. Some of them end up a little weird, but I usually have no way of knowing that beforehand, although face it, there are time when you just know a discussion is going nowhere good. I am not one to become uncomfortable or apprehensive too often, as you might guess from my avitar, which is actually quite accurate.

About the time a conversation gets to the point where my partner in crime (all conversations take two) is half way into a rant about a super computer hidden underground in Holland that records everything everyone does every day, I usually decide it's time to check out. "OK, that's nice, I gotta go now", and off I go. Just like that.

http://www.youtube.com/watch?v=awi14wDTxNw

I tend to give them a vague smile and then walk away. If the person is a stranger, I do not feel obligated to spin some polite white lie, especially if I did not invite the conversation in the first place. Some might feel that is rude, but in my opinion, being expected to share thoughts and conversation with someone I have never met is a little rude in and of itself. I never verbally berate the person or flat out tell them to stop talking to me. Walking away takes care of the need for that.