If your site is only meant for human end users, you can get lists of datacenter IPs and use that to block them (assuming they are running in a datacenter that's on the list). That tends to block all sorts of abuse.

If you are worried about blocking legit users with this method, you can show a CAPTCHA instead on every request from a suspect IP.

At any rate, get their IP from your logs and run a whois on it to get their ISP and location. You could also try emailing the ISP's abuse contact or filing a DMCA complaint with their hosting provider, although of course that might not work.