"Odd" generally means something mildly surprising or simply different. "Weird" suggests something very unusual or even mysterious (ie. strange, and without an explanation why).

Yep. "Weird" is more slangish, but it's still very commonly used. If you read old texts, you might see "weird“ being used to mean "supernatural” (ex. "weird sisters" for "witches"). This is not a modern definition and I've only ever seen it used in Shakespeare's texts. When my class came across this usage when reading Shakespeare in our final year of high school, no one except the teacher knew that "weird" could be used this way. Nonetheless, this is listed as the primary definition of "weird" in the dictionary, and the more common, modern usage is listed as informal.

Yes, but weird is usually a lot 'odder' than odd. e.g. A:there's a guy walking around out on the road wearing only his underpants B:that's odd A:And a chicken taped to his head B:that's weird!