I have a website that provides whois information.
How can I prevent that other websites use that information as a service? (using includes, string manipulation or whatever)
And if this is not possible, how can I tell which websites are using/including that information?
I take it your own website responds to WHOIS queries, delivering the information to clients/users (although you were ambiguous and may just be referring to your own whois entry, in which case you need a domain registration proxy).
The solution, then, is simple. Just limit the rate at which any IP address can make a query. Make it something that a normal user will likely never hit, but that a web site could not possibly operate with. Maybe one request every 5 (or whatever) seconds is a good place to start. Tighten the limit if you, for some reason, have problems.
Even if it doesn’t stop a website from pumping your API, it will slow them down so the strain on your server is negligible.
This can be used in addition to a daily limit and a modicum amount of log inspection. Manually ban IPs with suspicious activity and/or get some log monitoring software.