How can I tell if the odd things in my life are real?

Odd things? I'm not sure what kind of "odd things" you're talking about . . . . So it's hard to answer this question from here. It might help you more to talk with a therapist more specifically and fully about your concerns. Many people experience synchronicity, and it adds to their sense of purpose and meaning in life. But it's not clear that this is what you mean.
Involve others. The best sign indicating you can figure it out is your willingness to question the reality of those "odd" things. Ask family and friends your trust implicitly about it. Ask your physician or other health professional you trust. Don't wait! these "odd" things can be signs of a serious neurological or psychiatric problem best handled professionally.