Hi Vinnia, I have lived here in Evansville my entire life as well as bought and sold many SFH as well as holding a few rentals. I believe you have your zip codes mixed up The 100 block of E. Powell is actually in the 47713 zip code. That block is right on the border line of the downtown area which is currently being renovated over the last couple of years. If the renovations continue (I believe they will) to push east toward that block of Powell, I can see the property values increasing. I believe there are several multi units on that block.
The N. Sherman block you speak of, the addresses are actually the 2000's, not the 200's and the zip code is 47711. That is a solid rental & even a good flip area if you can pick up a SF for a good price. I have one about a couple miles away, but in a worse neighborhood.
47720 is on the far west side of town, and you are correct, not as many renters in that area compared to the other areas you mentioned.