What is the use of 的是?
的 (refer to definition 2 in this dictionary)


  
  代替所指的人或物：唱歌～。
  


我觉得奇怪的 here refers to things I feel weird. 

So, 我觉得奇怪的是 could be interpreted as "things I feel weird are:" or "What I feel weird are:".