日本では奇妙なこと if you put "ha" there, it sounds like "things that seem to be odd particularly in Japan (but maybe not in other countries?) so i'd say 日本で奇妙なこと. without "ha", so that it means "things that seem to be odd to me in Japan.
日本で奇妙な自動販売機を示すオンラインの記事があります。as for this first sentence, i'd say 日本で奇妙な自動販売機「があるという」オンラインの記事「を見ました」。
それは、使用される下着の自動販売機「の事を書いてありました」sounds more natural :) oh, but i think this "使用される下着"part you wanted to say was "使用された後の下着, underwears that someone has already used, i guess. cuz 使用される下着 would mean just underwears that people use. so they could be brand new underwears and maybe there's nothing weird about that. although being able to buy underwears from vending machines in public might seem to be weird to you haha
生きたカニもあっ「た」i think you just missed typing た there though :)。それはおかしいですが、不思議だった。 the combination of the words おかしい and不思議 in that sentence is a bit odd(at least to me), cuz they both sound kind of "unusual, abnormal, rare", so it sounds too wordy? so i might say something like それは不思議に感じた。 or.. oh, maybe if you change the sentence like それはおかしく思えて、不思議だった。it sounds fine even though those words are still in the sentence.. (hmm, japanese is too complecated lol) or.. それはおかしくて、不思議に思った。well, there are a lot of ways to say the same thing. mine is just an example :)
きっと誰かがそれを削除するのでしょうか。 i didn't quite understand this part. you meant someone might delete the online article? if so, why? do you think the article should be deleted?
anyway, hope my comment helps at least a bit :) i'm not used to correcting people's entries here, so i might sound a bit odd here and there though :p good luck with your Japanese! :D