I suppose that depends on the kind of dragon. The Western, or European, dragon and the Eastern dragon(Chinese lung) are the two most commonly known. For weaknesses they all like sparkly objects, more specifically gems. The Eastern dragons are more attracted to pearls and opals.
Many dragons can also be pulled into a game of wits since they like riddles. You just have to make sure you're good at that since most dragons live longer than we do and probably know quite a few riddles.
For strengths, it would also depend. A lot of people would say fire-breathing right off the bat, but not all draconic species can breath fire. It's said there's even one that breathes ice so cold that it burns. Flight is also limited to certain species. Some have a certain degree of intelligence (depending on how long they live) that could also be considered a strength.
Although not 100% indestructible, dragon hide and scales are very tough and to certain species, acts as armor to protect its wearer.(notice i didn't say the wearer had to be dragon.)