How do I block incoming AIM IM messages from strangers?

I can't help you with the latter question about tracking down the identity of someone when you just have their AIM handle, but you might try Googling their handle + "AIM" or similar, and see if something surfaces. I surmise it won't, but you never know what people make available on the public Internet.

In terms of blocking unwanted AIM messages and chats from people who aren't already on your buddy list, that's exactly how I have my own AIM account set up because, well, I don't want to hear from all those weirdoes either!

For reasons I find inexplicable, the default settings in AIM are too permissive and you really do need to go in and fix things. Worse, you have to go to a couple of places to really set things as you want, starting with Edit --> Settings...:

Once you've chosen that, you'll see a settings window with a ton of tabs running down the left side. Your first stop is "General IM", where you need to change a default setting:

You unquestionably want to turn OFF "Auto-accept IMs from unknown senders". Really, I have no idea why anyone would want that to be enabled, but that's another story. Make sure it's not checked, then click on the "Privacy" tab:

The most important setting is on the top left: I strongly suggest your daughter have hers set to "Only allow users on my Buddy List" to block the IMs from unknown folk. As you can see, I take it even a step further and have an explicit list of who can communicate with me (I've masked their handles to protect their privacy, btw). Honestly, that's a bit of a pain since when I want to IM with someone new on AIM I have to go to this specific window and add them by hand, even if I initiate the chat, but when I can be logged in to AIM all day and never get one stray or unwanted message, it's worth it!

Also note that if it's a single user or small set of users that are bugging your daughter, she can drop them into her "block" list and never be bothered by them again. You can also block someone when you're right there in a chat window: just look for "Block" on the "People" menu:

That should help your daughter gain some privacy in the chaos rave that is AIM chat. Good luck to both of you!