Interest 是名词,意思是兴趣、爱好.好比说,"Learning new languages is one of my interests" (学习外语是我的兴趣/爱好之一）,一般来说这个人已经拥有这个爱好.
Interested 是形容词,用在形容一个人对某个东西或某种事情感兴趣.好比说,"I am interested in learning new languages" (我对学外语感兴趣),一般是指对未来有如此打算.
Interesting 也是形容词,主要用在形容一件东西或一件事有吸引力或者很奇特.好比说,"I find foreign languages very interesting" (我觉得外语很有意思）.
Interestingly 是副词,用法很难解释,一般形容一件事出乎想象.好比说,"Math has historically been my weakest subject,but interestingly enough,I find this problem set quite fascinating."