Use this phrase when something surprising or coincidental happens. For example, if a friend tells you that she recently got a new job, and you also got a new job recently, you can respond:

Strangely enough, I just started a new job last week!

Another example: someone asks you whether you've spoken to your brother lately. Usually you speak with him every week, but the last time you spoke to him was 3 weeks ago. You can say:

Strangely enough, no. I haven't heard from him for a few weeks.