SOLUTION: What number am I if the sum of my digits is 9, I am an odd number, I am greater than 100 and less than 700, and I am a power of 3?

 
Since you are a power of 3, then you are one of these:

31 = 3
32 = 9
33 = 27
34 = 81
35 = 243
36 = 729
37 = 2187

Since you are greater than 100 and less than 700, then
you can only be 243.

Yes, you are an odd number, but you didn't need to tell us that.

And yes, the sum of your digits is 9, since 2+4+3 = 9, but you 
didn't need to tell us that either. 

Edwin