Are reused glass jars ever fit for storing ground coffee? I'm looking for some small container to store small amounts of ground coffee. 

I have a lot of jars after some other things, like olives. 

Can they ever be fit for storing ground coffee? Is it possible to remove all side odours from them?

If so, how should I clean them before using them for coffee?

The original package is not very tight after opening, so the jar would better prevent the contact with the air...
The Short answer  to this is no. You should not use a glass jar for storing coffee. 

Why? The base of the answer can be found here: When Does Coffee Go Off?

Coffee goes stale relatively quickly, and the transfer to a glass jar will: 


Increase the coffee's interaction and exposure to oxygen 
Increase the coffee's exposure to light, which will cause rancidification of the oils


Furthermore, you should only be purchasing and storing whole bean coffee - as pre-ground coffee is already stale.